Simulation, power, and logistic regression
Peter Ralph
22 January 2018 – Advanced Biological Statistics
Outline
Uses of simulation
… applied to the hierarchical model.
Posterior predictive sampling.
Shrinkage: sharing information
Predicting binary outcomes from quantitative variables: Bayesian logistic regression
Back to baseball
From last time:
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &\sim \Beta(\mu_{p_i} \kappa_{p_i}, (1-\mu_{p_i})\kappa_{p_i}) \\ \mu &\sim \Beta(1, 1) \\ \kappa_p &\sim \Gam(0.1, 0.1) . \end{aligned}\]
pos_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
}
parameters {
real<lower=0, upper=1> theta[N];
real<lower=0, upper=1> mu[npos];
real<lower=0> kappa[npos];
}
model {
real alpha;
real beta;
hits ~ binomial(at_bats, theta);
for (i in 1:N) {
alpha = mu[position[i]] * kappa[position[i]];
beta = (1 - mu[position[i]]) * kappa[position[i]];
theta[i] ~ beta(alpha, beta);
}
mu ~ beta(1,1);
kappa ~ gamma(0.1,0.1);
} "batting <- read.csv("BattingAverage.csv", header=TRUE)
system.time(pos_fit <- stan(model_code=pos_model, chains=3, iter=100,
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos))))## user system elapsed
## 36.542 0.699 63.372Diagnostics
## Inference for Stan model: db775bca82d7fc39d379745fb39b0819.
## 3 chains, each with iter=100; warmup=50; thin=1;
## post-warmup draws per chain=50, total post-warmup draws=150.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.25 0.00 0.01 0.24 0.25 0.25 0.26 0.26 150 0.99
## mu[2] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 150 1.01
## mu[3] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 150 0.99
## mu[4] 0.24 0.00 0.01 0.23 0.24 0.24 0.24 0.25 150 1.00
## mu[5] 0.26 0.00 0.01 0.25 0.25 0.26 0.26 0.27 150 1.01
## mu[6] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 150 0.98
## mu[7] 0.13 0.00 0.01 0.12 0.13 0.13 0.13 0.15 32 1.09
## mu[8] 0.26 0.00 0.01 0.25 0.25 0.26 0.26 0.27 150 1.00
## mu[9] 0.25 0.00 0.01 0.23 0.24 0.25 0.25 0.26 143 0.99
## kappa[1] 108.37 1.88 23.05 67.67 93.56 107.63 122.63 158.14 150 1.04
## kappa[2] 104.02 1.76 21.53 67.90 88.54 100.81 118.35 158.38 150 0.99
## kappa[3] 100.08 1.77 21.70 60.05 85.40 99.20 112.81 148.72 150 0.99
## kappa[4] 93.96 2.68 18.69 60.14 80.98 93.51 105.65 134.80 49 1.04
## kappa[5] 100.10 2.87 23.01 66.84 85.37 95.12 113.20 157.17 64 1.00
## kappa[6] 109.72 1.85 20.04 74.22 97.73 108.44 121.05 151.00 117 0.99
## kappa[7] 58.73 7.73 15.33 36.00 47.45 58.14 67.02 93.41 4 1.24
## kappa[8] 117.57 2.09 25.64 74.24 100.18 114.65 132.04 170.47 150 1.03
## kappa[9] 90.86 2.18 24.45 53.10 72.15 89.07 102.94 147.77 125 1.02
##
## Samples were drawn using NUTS(diag_e) at Tue Jan 23 09:36:38 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Is it mixing?
Run longer!
system.time(pos_fit <- stan(model_code=pos_model, chains=3, iter=1000,
control=list(max_treedepth=15),
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos))))## user system elapsed
## 0.693 0.031 461.301## Inference for Stan model: db775bca82d7fc39d379745fb39b0819.
## 3 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1500.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.25 0.00 0.01 0.24 0.25 0.25 0.26 0.26 1069 1.00
## mu[2] 0.25 0.00 0.01 0.24 0.24 0.25 0.25 0.26 848 1.00
## mu[3] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 1032 1.00
## mu[4] 0.24 0.00 0.01 0.23 0.23 0.24 0.24 0.25 622 1.00
## mu[5] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 725 1.00
## mu[6] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 725 1.00
## mu[7] 0.13 0.00 0.01 0.12 0.12 0.13 0.13 0.14 155 1.01
## mu[8] 0.26 0.00 0.01 0.25 0.25 0.26 0.26 0.27 1134 1.01
## mu[9] 0.25 0.00 0.01 0.23 0.24 0.25 0.25 0.26 902 1.00
## kappa[1] 111.46 0.80 22.73 72.21 95.14 109.91 126.23 159.03 801 1.00
## kappa[2] 104.10 0.83 24.31 63.39 86.72 101.64 118.19 160.01 859 1.00
## kappa[3] 98.40 0.69 21.63 62.82 82.72 96.13 112.30 144.99 974 1.01
## kappa[4] 95.30 0.84 20.67 60.16 80.97 93.37 107.86 140.67 601 1.00
## kappa[5] 101.80 0.84 22.88 61.50 85.47 100.64 116.86 148.69 742 1.00
## kappa[6] 106.34 0.78 21.32 69.56 91.43 104.68 118.46 155.97 743 1.01
## kappa[7] 56.29 1.16 13.21 35.00 46.82 54.85 64.32 85.75 129 1.01
## kappa[8] 119.73 1.00 27.64 73.47 100.23 118.23 135.95 180.19 761 1.00
## kappa[9] 95.69 0.91 22.74 59.07 79.80 93.10 109.56 148.44 619 1.00
##
## Samples were drawn using NUTS(diag_e) at Tue Jan 23 09:44:21 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Is it mixing?
Let’s look at the results!
I like labels.
param_samples <- extract(pos_fit)
layout(matrix(1:9, ncol=3))
par(mar=c(4,3,1,1)+.1)
for (k in 1:9) {
hist(param_samples$mu[,k], main=levels(batting$PriPos)[k],
xlim=c(0, 0.4), xlab='batting average', ylab=expression(mu))
}
layout(matrix(1:9, ncol=3))
par(mar=c(4,3,1,1)+.1)
for (k in 1:9) {
hist(param_samples$kappa[,k], main=levels(batting$PriPos)[k],
xlab='batting average', ylab=expression(kappa))
}
What else do you want to know?
About \[\begin{aligned} \theta_i &: \text{individual $i$ batting averages} \\ \mu &: \text{position $p$ mean batting averages} \\ \kappa_p &: \text{position $p$ variability of batting averages} \end{aligned}\]
Do positions with more at-bats have higher batting averages?
To answer this, let’s find the posterior distribution of the difference in means (\(\mu_p\)) between two positions, 1st base, who have a lot of at-bats, and pitchers, who don’t.
To do this, we’ll use the random samples obtained with extract().
first_base_col <- which(levels(batting$PriPos) == "1st Base")
pitcher_col <- which(levels(batting$PriPos) == "Pitcher")
mu_diff <- param_samples$mu[,first_base_col] - param_samples$mu[,pitcher_col]The posterior mean of \(\mu_\text{1st base} - \mu_\text{pitcher}\) is 0.1235826; and the posterior SD is 0.008477. This is a very large difference, and we are very certain of this - our estimate of a 95% credible interval for the difference is from 0.1071786 to 0.1401361.
What position has the most consistent batting average?
Find the posterior distribution of SDs of \(\theta_i\)s, separately by position.
Stochastic minute
Exponential, and Gamma
If \(T \sim \Exp(\text{rate}=\lambda)\), then
\[\begin{aligned} \P\{ T \in dt \} = \lambda e^{-\lambda t} dt . \end{aligned}\]
\(T\) can be any nonnegative real number.
\(T\) is memoryless: \[\begin{aligned} \P\{ T > x + y \given T > x \} = \P\{ T > y \} . \end{aligned}\]
A machine produces \(n\) widgets per second; each widget has probability \(\lambda/n\) of being broken. The time until the first broken widget appears (in seconds) is approximately \(\sim \Exp(\lambda)\).
If \(S \sim \Gam(\text{shape}=\alpha, \text{rate}=\lambda)\), then
\[\begin{aligned} \P\{ S \in dt \} = \frac{\alpha^\lambda}{\Gamma(\alpha)} t^{\alpha - 1} e^{-\lambda t} dt . \end{aligned}\]
If \(T_1, \ldots, T_k\) are independent \(\Exp(\lambda)\), then \(S = T_1 + \cdots + T_k\) is \(\Gam(k, \lambda)\).
A machine produces \(n\) widgets per second; each widget has probability \(\lambda/n\) of being broken. The time until the \(k^\text{th}\) broken widget appears (in seconds) is approximately \(\sim \Gam(k, \lambda)\).
Simulation
Wouldn’t it be nice if we knew the truth?
Discuss:
Write down (on whiteboards) a procedure to simulate data that looks like the baseball data.
batting$post_mean <- colMeans(param_samples$theta)
batting$fake_hits <- rbinom(nrow(batting),
size=batting$AtBats,
prob=batting$post_mean)Option 1: By simulating draws from the posterior mean on \(\theta\). we can check that our model is accurately describing the data - here we plot the real data against data simulated under the posterior mean \(\theta\) values. They look similar, which is good.
But if we want to know if we’re accurately estimating \(\mu\) and \(\theta\), then we have to start with them, and simulate \(\theta\).
post_mean_mu <- colMeans(param_samples$mu)
post_mean_kappa <- colMeans(param_samples$kappa)
names(post_mean_mu) <- names(post_mean_kappa) <- levels(batting$PriPos)
batting$sim_theta <- rbeta(nrow(batting),
shape1=post_mean_mu[batting$PriPos] *
post_mean_kappa[batting$PriPos],
shape2=(1-post_mean_mu[batting$PriPos]) *
post_mean_kappa[batting$PriPos])
batting$sim_theta_hits <- rbinom(nrow(batting),
size=batting$AtBats,
prob=batting$sim_theta)Fit the model to the simulated data:
Can we estimate \(\mu\) and \(\kappa\)?
sim_samples <- extract(sim_fit)
layout(t(1:2))
boxplot(sim_samples$mu, main="posterior distribution of mu")
points(1:9, post_mean_mu, col='red', pch=20, cex=2)
boxplot(sim_samples$kappa, main="posterior distribution of kappa")
points(1:9, post_mean_kappa, col='red', pch=20, cex=2)
General questions with simulated data
- Does my statistical inference method work?
Do the credible intervals contain the true value?
(i.e., Is the method “well-calibrated”?)
They usually should.
How wide are credible intervals, typically?
This is (one kind of) statistical power.
Posterior predictive sampling
How to choose parameter values for simulation?
It depends, but one good choice is from the posterior distribution - then you can see how the model behaves with data close to the real data.
This is known as posterior predictive sampling.
Sharing power // Shrinkage
Example
Suppose that I have a large pot of coins that are all similar to each other. I flip each one ten times, and record the number of Heads. What is each coin’s probability of Heads?
Treated separately, we would be very uncertain about each coin.
Together, they should tell us very accurately what are likely values of \(\theta\).
This information can improve the estimate of each separate \(\theta\).
The more similar the coins are, the more information we gain.
Shrinkage and baseball
Some players were at bat very few times. How does the information about their position affect our inference about their batting averages?
batting$post_med <- colMedians(param_samples$theta)
batting$post_Q1 <- colQuantiles(param_samples$theta, probs=0.25)
batting$post_Q3 <- colQuantiles(param_samples$theta, probs=0.75)
pos_means <- colMeans(param_samples$mu)
names(pos_means) <- levels(batting$PriPos)
pos_means## 1st Base 2nd Base 3rd Base Catcher Center Field
## 0.2524944 0.2486243 0.2560179 0.2390597 0.2577180
## Left Field Pitcher Right Field Shortstop
## 0.2490896 0.1289117 0.2586441 0.2473216Pitchers had posterior mean \(\mu\) of 0.1289117
with(subset(batting[order(batting$post_med),], PriPos=="Pitcher"), {
plot(Hits / AtBats, main="Pitchers", xaxt='n', ylim=c(0, 0.4),
xlab='player', ylab="posterior median theta");
segments(x0=seq_along(Hits), y0=post_Q1, y1=post_Q3,
col=adjustcolor('red',0.5));
points(post_med, pch=20) })
abline(h=pos_means["Pitcher"], lwd=2, col=adjustcolor("blue", 0.5))
Catchers had posterior mean \(\mu\) of 0.2390597
with(subset(batting[order(batting$post_med),], PriPos=="Catcher"), {
plot(Hits / AtBats, main="Catchers", xaxt='n', ylim=c(0, 0.4),
xlab='player', ylab="posterior median theta");
segments(x0=seq_along(Hits), y0=post_Q1, y1=post_Q3,
col=adjustcolor('red',0.5));
points(post_med, pch=20) })
abline(h=pos_means["Catcher"], lwd=2, col=adjustcolor("blue", 0.5))
Is shrinkage here a good idea?
With simulated data, compare median absolute error for
posterior mean \(\theta_i\)
empirical batting average
How’d we do? Let’s look at the true values of \(\theta\) (we know because we generated them) against the posterior means. Red lines are 95% credible intervals.
post_sim_theta <- colMeans(sim_samples$theta)
plot(batting$sim_theta, post_sim_theta, type='n', xlab="true theta", ylab="posterior mean theta", ylim=c(0,0.4))
segments(x0=batting$sim_theta, col='red',
y0=colQuantiles(sim_samples$theta, probs=0.05),
y1=colQuantiles(sim_samples$theta, probs=0.95))
points(batting$sim_theta, post_sim_theta, pch=20)
abline(0, 1, lwd=3, col=adjustcolor('blue', 0.5))
Did we do better?
The mean absolute difference between the truth and
- posterior mean: 0.0255111
- empirical batting average (hits/at bats): 0.0895372
Using information about groups reduced our error by a factor of 4!
Logistic regression, a.k.a. metric predictors
Motivation
There’s a good bit more information available about the baseball players.
## Player PriPos Hits AtBats PlayerNumber PriPosNumber
## 1 Aaron Cunningham Left Field 17 97 198 7
## 2 Aaron Harang Pitcher 4 56 360 1
## 3 Aaron Hill 2nd Base 184 609 394 4
## 4 Aaron Laffey Pitcher 0 1 482 1
## 5 Aaron Loup Pitcher 0 1 522 1
## 6 Adam Dunn 1st Base 110 539 242 3
## playerID weight height bats birthYear debut finalGame
## 1 cunniaa01 215 71 R 1986 2008-08-31 2012-07-24
## 2 haranaa01 260 79 R 1978 2002-05-25 2015-10-03
## 3 hillaa01 200 71 R 1982 2005-05-20 2016-10-01
## 4 laffeaa01 190 71 L 1985 2007-08-04 2015-07-31
## 5 loupaa01 210 71 L 1987 2012-07-14 2016-09-30
## 6 dunnad01 285 78 L 1979 2001-07-20 2014-09-28Is batting average predicted by weight and height?
Each player has their own batting avg, \(\theta_i\).
Batting averages tend to be different for different positions.
After accounting for position (\(p_i\)), \(\theta\) varies with height (\(h_i\)) and/or weight (\(w_i\)).
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &= \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, \sigma_\gamma) \\ \alpha_h &\sim \Normal(0, \sigma_h) \\ \alpha_w &\sim \Normal(0, \sigma_w) \\ \sigma_\gamma, \sigma_h, \sigma_w &\sim \Normal^+(0, 20) \end{aligned}\]
Stan
logistic_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
vector[N] height;
vector[N] weight;
}
parameters {
real<lower=0, upper=1> theta[N];
vector[npos] gamma;
real alpha_w;
real alpha_h;
vector<lower=0>[npos] kappa;
}
model {
vector[N] mu;
mu = inv_logit(gamma[position] + alpha_h * height + alpha_w * weight);
theta ~ beta(mu .* kappa[position], (1-mu) .* kappa[position]);
hits ~ binomial(at_bats, theta);
kappa ~ gamma(0.1, 0.1);
gamma ~ normal(0, 5);
alpha_h ~ normal(0, 5);
alpha_w ~ normal(0, 5);
} "\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &= \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, 5) \\ \alpha_h &\sim \Normal(0, 5) \\ \alpha_w &\sim \Normal(0, 5) \end{aligned}\]
New features
logistic_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
vector[N] height;
vector[N] weight;
}
parameters {
real<lower=0, upper=1> theta[N];
vector[npos] gamma;
real alpha_w;
real alpha_h;
vector<lower=0>[npos] kappa;
}
model {
vector[N] mu;
mu = inv_logit(gamma[position] + alpha_h * height + alpha_w * weight);
theta ~ beta(mu .* kappa[position], (1-mu) .* kappa[position]);
hits ~ binomial(at_bats, theta);
kappa ~ gamma(0.1, 0.1);
gamma ~ normal(0, 5);
alpha_h ~ normal(0, 5);
alpha_w ~ normal(0, 5);
} "vector[N] height;instead ofreal height[N];: to allowalpha_h * height.we will center and scale height and weight before passing to Stan
x .* yfor component-wise multiplication
scaled_height <- (batplus$height - mean(batplus$height))/sd(batplus$height)
scaled_weight <- (batplus$weight - mean(batplus$weight))/sd(batplus$weight)
system.time(logistic_fit <- stan(model_code=logistic_model, chains=3, iter=1000,
control=list(adapt_delta=0.9, max_treedepth=12),
data=list(N=nrow(batplus),
hits=batplus$Hits,
at_bats=batplus$AtBats,
npos=nlevels(batplus$PriPos),
position=as.numeric(batplus$PriPos),
height=scaled_height,
weight=scaled_weight) ))## user system elapsed
## 0.824 0.558 194.307## mean se_mean sd 2.5%
## theta[1] 2.143570e-01 0.0007504409 0.02906445 1.586215e-01
## theta[2] 9.958646e-02 0.0007378431 0.02857654 4.985748e-02
## theta[3] 2.943555e-01 0.0004295569 0.01663667 2.623725e-01
## theta[4] 1.249136e-01 0.0011953081 0.04629408 5.033112e-02
## theta[5] 1.278615e-01 0.0012340461 0.04779440 5.241527e-02
## theta[6] 2.129775e-01 0.0004155144 0.01609280 1.821791e-01
## theta[7] 2.835363e-01 0.0004379097 0.01696017 2.507855e-01
## theta[8] 2.595330e-01 0.0007293775 0.02824867 2.069431e-01
## theta[9] 2.680070e-01 0.0004472417 0.01732160 2.341217e-01
## theta[10] 2.533847e-01 0.0005274577 0.02042835 2.128361e-01
## theta[11] 2.300007e-01 0.0010647855 0.04123897 1.530535e-01
## theta[12] 1.267037e-01 0.0011203416 0.04339064 5.559656e-02
## theta[13] 2.353814e-01 0.0007909022 0.03063151 1.784444e-01
## theta[14] 1.249213e-01 0.0007772488 0.03010272 7.099962e-02
## theta[15] 2.533472e-01 0.0007483862 0.02898487 1.994112e-01
## theta[16] 3.120121e-01 0.0004825431 0.01868881 2.776105e-01
## theta[17] 2.252824e-01 0.0008657700 0.03353113 1.621427e-01
## theta[18] 2.924380e-01 0.0004475392 0.01733312 2.594596e-01
## theta[19] 2.445125e-01 0.0009315818 0.03608001 1.754849e-01
## theta[20] 2.808342e-01 0.0004355895 0.01687031 2.478609e-01
## theta[21] 2.540070e-01 0.0004802154 0.01859866 2.188846e-01
## theta[22] 2.445329e-01 0.0009208881 0.03566584 1.773203e-01
## theta[23] 2.865473e-01 0.0004352074 0.01685551 2.534540e-01
## theta[24] 2.771984e-01 0.0004589328 0.01777439 2.424858e-01
## theta[25] 2.423038e-01 0.0005095967 0.01973660 2.039061e-01
## theta[26] 2.342584e-01 0.0009478115 0.03670858 1.651822e-01
## theta[27] 2.884781e-01 0.0004455814 0.01725729 2.537397e-01
## theta[28] 1.220974e-01 0.0011298825 0.04376016 5.111752e-02
## theta[29] 2.386450e-01 0.0007441211 0.02881968 1.845494e-01
## theta[30] 2.394652e-01 0.0005125019 0.01984911 2.003212e-01
## theta[31] 2.973474e-01 0.0004241304 0.01642650 2.665083e-01
## theta[32] 2.693900e-01 0.0004956071 0.01919478 2.322872e-01
## theta[33] 1.470093e-01 0.0010430878 0.04039862 7.755719e-02
## theta[34] 2.623852e-01 0.0004345754 0.01683103 2.318962e-01
## theta[35] 2.433457e-01 0.0006014124 0.02329260 1.992568e-01
## theta[36] 2.424885e-01 0.0005577109 0.02160005 2.012154e-01
## theta[37] 1.428546e-01 0.0012088227 0.04681750 6.435940e-02
## theta[38] 2.594585e-01 0.0004668651 0.01808161 2.244004e-01
## theta[39] 1.233807e-01 0.0011142408 0.04315436 5.108786e-02
## theta[40] 2.276062e-01 0.0010913184 0.04226658 1.499009e-01
## theta[41] 2.964684e-01 0.0005088205 0.01970653 2.601872e-01
## theta[42] 2.800899e-01 0.0004646486 0.01799576 2.464989e-01
## theta[43] 2.731184e-01 0.0007265596 0.02813953 2.199992e-01
## theta[44] 2.357835e-01 0.0005230637 0.02025817 1.968475e-01
## theta[45] 1.305839e-01 0.0011049119 0.04279305 5.599148e-02
## theta[46] 3.181786e-01 0.0004742089 0.01836603 2.833922e-01
## theta[47] 2.752487e-01 0.0011915254 0.04614758 1.909747e-01
## theta[48] 1.211242e-01 0.0010521502 0.04074960 5.443379e-02
## theta[49] 2.141128e-01 0.0005493254 0.02127528 1.756088e-01
## theta[50] 3.022576e-01 0.0005720290 0.02215459 2.615357e-01
## theta[51] 2.233610e-01 0.0007431619 0.02878254 1.697726e-01
## theta[52] 1.384479e-01 0.0012197147 0.04723935 6.126925e-02
## theta[53] 1.509725e-01 0.0013049485 0.05054044 6.794572e-02
## theta[54] 2.832269e-01 0.0004187715 0.01621895 2.526359e-01
## theta[55] 1.178599e-01 0.0009168793 0.03551058 5.939418e-02
## theta[56] 1.290592e-01 0.0009707798 0.03759814 6.335859e-02
## theta[57] 2.352586e-01 0.0006773141 0.02623226 1.847267e-01
## theta[58] 2.057062e-01 0.0008762130 0.03393558 1.420357e-01
## theta[59] 2.779126e-01 0.0005398854 0.02090967 2.367320e-01
## theta[60] 1.248889e-01 0.0011525426 0.04463778 5.198667e-02
## theta[61] 2.940414e-01 0.0004576773 0.01772577 2.596523e-01
## theta[62] 1.130613e-01 0.0010941707 0.04237705 4.473921e-02
## theta[63] 2.675320e-01 0.0004373221 0.01693741 2.355408e-01
## theta[64] 2.263994e-01 0.0007834984 0.03034476 1.694624e-01
## theta[65] 2.938628e-01 0.0004672524 0.01809661 2.594771e-01
## theta[66] 2.485149e-01 0.0007029669 0.02722579 1.980316e-01
## theta[67] 2.794346e-01 0.0009461644 0.03664479 2.135490e-01
## theta[68] 1.297302e-01 0.0012017888 0.04654508 5.150712e-02
## theta[69] 1.019625e-01 0.0007963479 0.03084242 4.958265e-02
## theta[70] 1.295223e-01 0.0012406768 0.04805121 5.113465e-02
## theta[71] 2.456421e-01 0.0006849401 0.02652761 1.957109e-01
## theta[72] 2.862542e-01 0.0004876344 0.01888600 2.496157e-01
## theta[73] 1.019914e-01 0.0009803920 0.03797042 3.978784e-02
## theta[74] 2.669469e-01 0.0004299638 0.01665243 2.334802e-01
## theta[75] 3.057237e-01 0.0004302920 0.01666514 2.738841e-01
## theta[76] 1.267070e-01 0.0011499949 0.04453911 5.185606e-02
## theta[77] 2.254981e-01 0.0009343265 0.03618631 1.560280e-01
## theta[78] 2.209148e-01 0.0010541725 0.04082793 1.445424e-01
## theta[79] 2.293382e-01 0.0010382645 0.04021181 1.544545e-01
## theta[80] 2.454506e-01 0.0006016922 0.02330344 2.019295e-01
## theta[81] 2.213182e-01 0.0006466227 0.02504359 1.749166e-01
## theta[82] 1.281195e-01 0.0012781752 0.04950351 5.103948e-02
## theta[83] 1.292850e-01 0.0012335360 0.04777464 5.154029e-02
## theta[84] 1.266120e-01 0.0011773000 0.04559663 4.968206e-02
## theta[85] 1.432888e-01 0.0011657143 0.04514792 6.676191e-02
## theta[86] 1.319983e-01 0.0011889613 0.04604827 5.568465e-02
## theta[87] 1.386524e-01 0.0011935273 0.04622511 6.461809e-02
## theta[88] 2.294508e-01 0.0009910004 0.03838128 1.581689e-01
## theta[89] 2.303312e-01 0.0007696884 0.02980990 1.735026e-01
## theta[90] 1.491387e-01 0.0010444788 0.04045249 7.954226e-02
## theta[91] 2.698419e-01 0.0004992739 0.01933679 2.345121e-01
## theta[92] 2.483308e-01 0.0004852023 0.01879181 2.129766e-01
## theta[93] 1.422482e-01 0.0013239149 0.05127500 5.675357e-02
## theta[94] 1.252106e-01 0.0011928377 0.04619841 5.071847e-02
## theta[95] 2.387120e-01 0.0010658640 0.04128074 1.643978e-01
## theta[96] 2.159380e-01 0.0008816932 0.03414783 1.557851e-01
## theta[97] 2.269002e-01 0.0005065842 0.01961992 1.881913e-01
## theta[98] 2.553540e-01 0.0010396323 0.04026479 1.791463e-01
## theta[99] 2.791754e-01 0.0006324427 0.02449440 2.333410e-01
## theta[100] 2.764522e-01 0.0004695804 0.01818677 2.417502e-01
## theta[101] 2.624942e-01 0.0009000277 0.03485792 1.980058e-01
## theta[102] 2.383814e-01 0.0006322878 0.02448840 1.932975e-01
## theta[103] 2.033959e-01 0.0004705428 0.01822405 1.691563e-01
## theta[104] 2.437639e-01 0.0004937407 0.01912249 2.086969e-01
## theta[105] 2.138613e-01 0.0006318709 0.02447226 1.687165e-01
## theta[106] 2.141345e-01 0.0007605157 0.02945465 1.581932e-01
## theta[107] 2.543049e-01 0.0012436965 0.04816816 1.676127e-01
## theta[108] 1.265217e-01 0.0011502242 0.04454799 5.463946e-02
## theta[109] 2.640489e-01 0.0010031056 0.03885011 1.913185e-01
## theta[110] 2.172851e-01 0.0007736597 0.02996371 1.623136e-01
## theta[111] 2.120738e-01 0.0007226114 0.02798662 1.593961e-01
## theta[112] 2.704212e-01 0.0004555248 0.01764240 2.381611e-01
## theta[113] 2.301899e-01 0.0007950972 0.03079398 1.768346e-01
## theta[114] 2.554072e-01 0.0006253208 0.02421857 2.108564e-01
## theta[115] 2.272916e-01 0.0007995276 0.03096557 1.699470e-01
## theta[116] 2.160646e-01 0.0005057371 0.01958711 1.782451e-01
## theta[117] 2.375255e-01 0.0005119104 0.01982621 1.994743e-01
## theta[118] 1.273077e-01 0.0012337652 0.04778352 4.691320e-02
## theta[119] 1.346937e-01 0.0011887844 0.04604142 5.603021e-02
## theta[120] 2.313900e-01 0.0004755715 0.01841880 1.966986e-01
## theta[121] 2.220855e-01 0.0008284186 0.03208452 1.629910e-01
## theta[122] 1.244757e-01 0.0012396758 0.04801244 4.474553e-02
## theta[123] 2.317253e-01 0.0008109464 0.03140782 1.725721e-01
## theta[124] 2.666731e-01 0.0008860633 0.03431708 2.026277e-01
## theta[125] 1.354843e-01 0.0008173370 0.03165532 8.267498e-02
## theta[126] 1.930604e-01 0.0007200667 0.02788806 1.412947e-01
## theta[127] 1.396942e-01 0.0011544019 0.04470979 6.528582e-02
## theta[128] 1.372311e-01 0.0011808108 0.04573261 6.182320e-02
## theta[129] 2.375790e-01 0.0011430531 0.04427025 1.534152e-01
## theta[130] 2.386914e-01 0.0011079550 0.04291091 1.595005e-01
## theta[131] 2.565618e-01 0.0005558575 0.02152827 2.175893e-01
## theta[132] 2.117350e-01 0.0005304889 0.02054575 1.726484e-01
## theta[133] 2.686774e-01 0.0004504475 0.01744576 2.346528e-01
## theta[134] 1.158916e-01 0.0008159382 0.03160115 6.177694e-02
## theta[135] 1.256704e-01 0.0012392434 0.04799569 4.767207e-02
## theta[136] 3.211865e-01 0.0004856697 0.01880991 2.842405e-01
## theta[137] 2.450354e-01 0.0004647038 0.01799790 2.114879e-01
## theta[138] 2.673839e-01 0.0007860375 0.03044310 2.069473e-01
## theta[139] 1.291168e-01 0.0012743821 0.04935661 4.916216e-02
## theta[140] 2.671145e-01 0.0004432924 0.01716864 2.339088e-01
## theta[141] 2.552658e-01 0.0008516121 0.03298280 1.950327e-01
## theta[142] 2.595088e-01 0.0005161674 0.01999108 2.208328e-01
## theta[143] 2.939536e-01 0.0004912619 0.01902649 2.574862e-01
## theta[144] 2.637393e-01 0.0004470832 0.01731546 2.312413e-01
## theta[145] 2.356745e-01 0.0008863450 0.03432799 1.713490e-01
## theta[146] 2.065156e-01 0.0004310579 0.01669480 1.751133e-01
## theta[147] 2.585944e-01 0.0005781888 0.02239316 2.162149e-01
## theta[148] 3.079950e-01 0.0005810667 0.02250462 2.654802e-01
## theta[149] 2.498294e-01 0.0004635823 0.01795447 2.153943e-01
## theta[150] 1.423882e-01 0.0011520375 0.04461822 6.738354e-02
## theta[151] 2.448357e-01 0.0010587018 0.04100335 1.688804e-01
## theta[152] 1.462973e-01 0.0013031408 0.05047043 6.307771e-02
## theta[153] 1.530866e-01 0.0010132291 0.03924219 8.319841e-02
## theta[154] 1.396509e-01 0.0012105563 0.04688464 6.153332e-02
## theta[155] 1.417778e-01 0.0011996083 0.04646063 6.387698e-02
## theta[156] 2.328973e-01 0.0004669368 0.01808438 1.993924e-01
## theta[157] 2.259051e-01 0.0005160527 0.01998664 1.875837e-01
## theta[158] 2.335226e-01 0.0005480238 0.02122487 1.930808e-01
## theta[159] 1.252072e-01 0.0011296986 0.04375304 5.102618e-02
## theta[160] 2.437254e-01 0.0006958670 0.02695081 1.937842e-01
## theta[161] 1.255274e-01 0.0011986680 0.04642421 4.931988e-02
## theta[162] 1.591568e-01 0.0009982216 0.03866096 9.093671e-02
## theta[163] 1.108054e-01 0.0011010027 0.04264165 3.901209e-02
## theta[164] 2.597247e-01 0.0007804753 0.03022768 2.035103e-01
## theta[165] 2.702791e-01 0.0007958301 0.03082237 2.130699e-01
## theta[166] 2.290104e-01 0.0009899869 0.03834203 1.581879e-01
## theta[167] 2.821410e-01 0.0004431666 0.01716377 2.496518e-01
## theta[168] 2.541383e-01 0.0005512985 0.02135170 2.122356e-01
## theta[169] 2.804264e-01 0.0005078875 0.01967040 2.436903e-01
## theta[170] 2.071700e-01 0.0006628227 0.02567101 1.593478e-01
## theta[171] 1.194747e-01 0.0011378223 0.04406767 4.745114e-02
## theta[172] 1.120957e-01 0.0008123761 0.03146319 5.849351e-02
## theta[173] 1.961965e-01 0.0007522584 0.02913484 1.428741e-01
## theta[174] 2.674349e-01 0.0004358853 0.01688177 2.353080e-01
## theta[175] 2.848330e-01 0.0005586052 0.02163469 2.422031e-01
## theta[176] 2.541732e-01 0.0010633636 0.04118389 1.765700e-01
## theta[177] 2.652963e-01 0.0006447854 0.02497243 2.188198e-01
## theta[178] 2.514947e-01 0.0008173469 0.03165571 1.890580e-01
## theta[179] 2.606743e-01 0.0005052979 0.01957010 2.230820e-01
## theta[180] 2.064107e-01 0.0010015451 0.03878967 1.334804e-01
## theta[181] 2.397611e-01 0.0006246446 0.02419238 1.948756e-01
## theta[182] 2.764872e-01 0.0004710630 0.01824419 2.439016e-01
## theta[183] 1.265329e-01 0.0011452821 0.04435659 5.493264e-02
## theta[184] 1.213877e-01 0.0011976105 0.04638325 4.426380e-02
## theta[185] 2.911000e-01 0.0005361400 0.02076461 2.501889e-01
## theta[186] 2.382451e-01 0.0006130897 0.02374486 1.927718e-01
## theta[187] 1.219808e-01 0.0011094167 0.04296752 5.111799e-02
## theta[188] 1.341159e-01 0.0011371467 0.04404150 6.346770e-02
## theta[189] 1.196815e-01 0.0012729095 0.04929957 4.038094e-02
## theta[190] 1.400290e-01 0.0012126047 0.04696398 6.152774e-02
## theta[191] 1.938897e-01 0.0005923153 0.02294027 1.502420e-01
## theta[192] 2.384768e-01 0.0007431357 0.02878152 1.854033e-01
## theta[193] 1.472872e-01 0.0010277549 0.03980477 8.080564e-02
## theta[194] 1.120524e-01 0.0009221752 0.03571569 4.944579e-02
## theta[195] 1.224377e-01 0.0011800455 0.04570297 4.557726e-02
## theta[196] 1.277618e-01 0.0012496734 0.04839964 4.562994e-02
## theta[197] 1.718588e-01 0.0009464208 0.03665472 1.073638e-01
## theta[198] 1.234648e-01 0.0011686473 0.04526151 4.974637e-02
## theta[199] 1.046930e-01 0.0007049017 0.02730073 5.891012e-02
## theta[200] 2.337418e-01 0.0009944492 0.03851485 1.608999e-01
## theta[201] 2.208468e-01 0.0004498755 0.01742360 1.882474e-01
## theta[202] 2.318582e-01 0.0004870973 0.01886520 1.972310e-01
## theta[203] 2.593871e-01 0.0005191107 0.02010507 2.193841e-01
## theta[204] 2.267450e-01 0.0005697635 0.02206685 1.843680e-01
## theta[205] 2.651060e-01 0.0004731584 0.01832534 2.297054e-01
## theta[206] 1.590164e-01 0.0013493327 0.05225943 7.242311e-02
## theta[207] 2.277070e-01 0.0004010171 0.01553132 1.966425e-01
## theta[208] 1.788217e-01 0.0009429448 0.03652010 1.115281e-01
## theta[209] 2.587040e-01 0.0007740618 0.02997929 2.014596e-01
## theta[210] 1.186506e-01 0.0011080665 0.04291523 4.785690e-02
## theta[211] 2.346608e-01 0.0010209931 0.03954289 1.601628e-01
## theta[212] 2.407702e-01 0.0009186600 0.03557955 1.715374e-01
## theta[213] 2.381415e-01 0.0009496987 0.03678167 1.661688e-01
## theta[214] 2.679456e-01 0.0004380387 0.01696517 2.369599e-01
## theta[215] 1.265973e-01 0.0011570943 0.04481407 5.155831e-02
## theta[216] 1.059714e-01 0.0009587434 0.03713197 4.341003e-02
## theta[217] 1.212989e-01 0.0011322450 0.04385166 5.068163e-02
## theta[218] 2.913528e-01 0.0006546004 0.02535257 2.442474e-01
## theta[219] 1.179856e-01 0.0011433495 0.04428173 4.568529e-02
## theta[220] 1.198163e-01 0.0011573589 0.04482432 4.698442e-02
## theta[221] 2.350339e-01 0.0004202535 0.01627635 2.052515e-01
## theta[222] 1.254990e-01 0.0012406117 0.04804868 4.926379e-02
## theta[223] 1.212379e-01 0.0009821757 0.03803950 5.657994e-02
## theta[224] 1.208224e-01 0.0011732608 0.04544020 4.528721e-02
## theta[225] 1.292333e-01 0.0012279357 0.04755774 4.913755e-02
## theta[226] 2.710005e-01 0.0010335265 0.04002831 1.977007e-01
## theta[227] 1.272181e-01 0.0012423365 0.04811548 4.964986e-02
## theta[228] 2.253401e-01 0.0004168956 0.01614630 1.939933e-01
## theta[229] 1.227470e-01 0.0011429480 0.04426618 4.913396e-02
## theta[230] 2.325583e-01 0.0004947340 0.01916096 1.933912e-01
## theta[231] 1.362422e-01 0.0010821114 0.04190999 6.316168e-02
## theta[232] 2.843903e-01 0.0004615120 0.01787428 2.504414e-01
## theta[233] 2.445918e-01 0.0005776463 0.02237214 2.025409e-01
## theta[234] 2.481507e-01 0.0004248977 0.01645622 2.170349e-01
## theta[235] 2.136304e-01 0.0006826072 0.02643726 1.630489e-01
## theta[236] 2.350711e-01 0.0008203602 0.03177242 1.737961e-01
## theta[237] 2.281327e-01 0.0006964623 0.02697387 1.785665e-01
## theta[238] 2.541954e-01 0.0006960843 0.02695923 2.041679e-01
## theta[239] 2.737746e-01 0.0009876165 0.03825022 2.023296e-01
## theta[240] 2.286711e-01 0.0007650838 0.02963157 1.744617e-01
## theta[241] 2.528794e-01 0.0004700320 0.01820426 2.177672e-01
## theta[242] 2.655999e-01 0.0008686959 0.03364445 2.035154e-01
## theta[243] 2.795228e-01 0.0007252949 0.02809055 2.264570e-01
## theta[244] 2.620385e-01 0.0004547587 0.01761273 2.286709e-01
## theta[245] 2.879187e-01 0.0004779643 0.01851148 2.527745e-01
## theta[246] 1.509563e-01 0.0012997315 0.05033839 7.025030e-02
## theta[247] 1.260771e-01 0.0011988365 0.04643074 4.653027e-02
## theta[248] 2.482900e-01 0.0009147473 0.03542801 1.798501e-01
## theta[249] 2.926073e-01 0.0004978579 0.01928195 2.554265e-01
## theta[250] 3.023484e-01 0.0006062516 0.02348002 2.582840e-01
## theta[251] 1.190850e-01 0.0011510153 0.04457863 4.603783e-02
## theta[252] 2.494582e-01 0.0006662793 0.02580489 2.019808e-01
## theta[253] 2.983649e-01 0.0004286684 0.01660226 2.658193e-01
## theta[254] 2.557919e-01 0.0004391589 0.01700855 2.239488e-01
## theta[255] 2.311698e-01 0.0005515239 0.02136043 1.910724e-01
## theta[256] 2.640552e-01 0.0004405945 0.01706415 2.319766e-01
## theta[257] 2.794893e-01 0.0004684629 0.01814349 2.457745e-01
## theta[258] 2.646731e-01 0.0012097440 0.04685318 1.797922e-01
## theta[259] 1.259416e-01 0.0012113949 0.04691712 4.813631e-02
## theta[260] 3.082347e-01 0.0004525932 0.01752886 2.727944e-01
## theta[261] 1.582457e-01 0.0013333568 0.05164069 7.462599e-02
## theta[262] 2.128135e-01 0.0006552023 0.02537587 1.669503e-01
## theta[263] 2.453560e-01 0.0004511247 0.01747199 2.117650e-01
## theta[264] 2.212853e-01 0.0007082989 0.02743230 1.711474e-01
## theta[265] 2.554965e-01 0.0006241644 0.02417378 2.075108e-01
## theta[266] 2.924602e-01 0.0005069444 0.01963387 2.559393e-01
## theta[267] 2.585271e-01 0.0011127785 0.04309773 1.771947e-01
## theta[268] 1.363416e-01 0.0009991250 0.03869594 7.014375e-02
## theta[269] 2.626711e-01 0.0009403965 0.03642140 1.974396e-01
## theta[270] 2.829637e-01 0.0006627967 0.02567001 2.347885e-01
## theta[271] 2.430377e-01 0.0006560059 0.02540700 1.952014e-01
## theta[272] 2.202606e-01 0.0007336108 0.02841262 1.650007e-01
## theta[273] 2.329157e-01 0.0007367526 0.02853430 1.767435e-01
## theta[274] 2.834986e-01 0.0006048100 0.02342419 2.405971e-01
## theta[275] 1.220619e-01 0.0011609841 0.04496472 4.500934e-02
## theta[276] 2.153679e-01 0.0007596899 0.02942266 1.602656e-01
## theta[277] 1.246852e-01 0.0011381791 0.04408149 5.011702e-02
## theta[278] 1.645706e-01 0.0011709981 0.04535256 8.997347e-02
## theta[279] 1.251149e-01 0.0012368065 0.04790131 4.812544e-02
## theta[280] 2.199621e-01 0.0004443284 0.01720876 1.865192e-01
## theta[281] 2.498296e-01 0.0007106479 0.02752327 1.962576e-01
## theta[282] 1.249906e-01 0.0011593902 0.04490299 5.150051e-02
## theta[283] 2.292383e-01 0.0004090185 0.01584122 1.987227e-01
## theta[284] 1.266989e-01 0.0012106555 0.04688849 4.895648e-02
## theta[285] 2.832069e-01 0.0004496872 0.01741631 2.504148e-01
## theta[286] 1.007540e-01 0.0007726087 0.02992301 4.931888e-02
## theta[287] 2.309185e-01 0.0007422662 0.02874785 1.755715e-01
## theta[288] 2.695750e-01 0.0009142947 0.03541048 2.070782e-01
## theta[289] 1.248751e-01 0.0011705494 0.04533518 4.877245e-02
## theta[290] 2.767733e-01 0.0004439289 0.01719329 2.451680e-01
## theta[291] 1.821115e-01 0.0009796409 0.03794133 1.161798e-01
## theta[292] 2.467344e-01 0.0009365092 0.03627084 1.781370e-01
## theta[293] 2.219348e-01 0.0010442141 0.04044224 1.477671e-01
## theta[294] 2.516738e-01 0.0006467941 0.02505023 2.047998e-01
## theta[295] 2.436258e-01 0.0005681724 0.02200522 2.029101e-01
## theta[296] 1.249360e-01 0.0012102480 0.04687270 4.764912e-02
## theta[297] 2.814889e-01 0.0004431471 0.01716301 2.463847e-01
## theta[298] 2.590161e-01 0.0006170927 0.02389990 2.139296e-01
## theta[299] 2.278072e-01 0.0006802760 0.02634698 1.773578e-01
## theta[300] 2.190926e-01 0.0006890549 0.02668698 1.692248e-01
## theta[301] 2.743143e-01 0.0005798651 0.02245808 2.304007e-01
## theta[302] 2.387098e-01 0.0010721797 0.04152534 1.645066e-01
## theta[303] 2.498705e-01 0.0011012735 0.04265214 1.705206e-01
## theta[304] 1.257586e-01 0.0011857996 0.04592582 5.108099e-02
## theta[305] 2.220211e-01 0.0006887945 0.02667690 1.708842e-01
## theta[306] 2.353911e-01 0.0004303358 0.01666683 2.032687e-01
## theta[307] 2.048548e-01 0.0007699644 0.02982059 1.474030e-01
## theta[308] 1.724635e-01 0.0011119723 0.04306650 9.995612e-02
## theta[309] 2.375654e-01 0.0005461625 0.02115278 1.964666e-01
## theta[310] 2.838856e-01 0.0004770643 0.01847662 2.504630e-01
## theta[311] 1.200210e-01 0.0008981132 0.03478377 6.042642e-02
## theta[312] 2.416420e-01 0.0008779949 0.03400460 1.788475e-01
## theta[313] 2.451375e-01 0.0007365848 0.02852781 1.892857e-01
## theta[314] 1.168258e-01 0.0010850173 0.04202254 4.862687e-02
## theta[315] 1.391789e-01 0.0011818160 0.04577154 6.441212e-02
## theta[316] 2.535864e-01 0.0011903001 0.04610012 1.689489e-01
## theta[317] 2.806135e-01 0.0005973185 0.02313405 2.369537e-01
## theta[318] 2.471119e-01 0.0005236482 0.02028081 2.095608e-01
## theta[319] 2.602426e-01 0.0007106401 0.02752297 2.073621e-01
## theta[320] 1.305345e-01 0.0012174497 0.04715163 5.270021e-02
## theta[321] 1.426389e-01 0.0012134397 0.04699632 6.328312e-02
## theta[322] 1.336040e-01 0.0011513190 0.04459039 6.090205e-02
## theta[323] 2.428690e-01 0.0007292593 0.02824409 1.898438e-01
## theta[324] 1.236497e-01 0.0011505564 0.04456086 4.923965e-02
## theta[325] 1.269896e-01 0.0012264959 0.04750198 4.712790e-02
## theta[326] 2.340456e-01 0.0012191263 0.04721656 1.453731e-01
## theta[327] 1.232116e-01 0.0011677628 0.04522726 4.831100e-02
## theta[328] 2.371294e-01 0.0010076487 0.03902607 1.677369e-01
## theta[329] 2.586466e-01 0.0007479482 0.02896791 2.054814e-01
## theta[330] 1.442133e-01 0.0013432417 0.05202353 5.735453e-02
## theta[331] 2.577098e-01 0.0004441065 0.01720017 2.254938e-01
## theta[332] 2.343027e-01 0.0006475450 0.02507931 1.853884e-01
## theta[333] 2.266455e-01 0.0005143507 0.01992072 1.886157e-01
## theta[334] 2.696904e-01 0.0004667439 0.01807691 2.352533e-01
## theta[335] 1.246271e-01 0.0011938926 0.04623926 5.055901e-02
## theta[336] 1.293922e-01 0.0012524514 0.04850723 5.212080e-02
## theta[337] 2.296630e-01 0.0010235771 0.03964297 1.542241e-01
## theta[338] 1.255721e-01 0.0012243353 0.04741830 4.826063e-02
## theta[339] 2.195597e-01 0.0006490829 0.02513887 1.704388e-01
## theta[340] 2.070295e-01 0.0005022023 0.01945021 1.689194e-01
## theta[341] 2.677722e-01 0.0006883091 0.02665810 2.185195e-01
## theta[342] 2.704769e-01 0.0005111873 0.01979820 2.329853e-01
## theta[343] 2.837952e-01 0.0005077985 0.01966695 2.459371e-01
## theta[344] 2.429911e-01 0.0009169520 0.03551340 1.766835e-01
## theta[345] 1.105369e-01 0.0007642002 0.02959735 5.768393e-02
## theta[346] 2.367114e-01 0.0004461906 0.01728089 2.044451e-01
## theta[347] 2.165077e-01 0.0007113739 0.02755139 1.644379e-01
## theta[348] 1.247832e-01 0.0011666865 0.04518558 4.946878e-02
## theta[349] 2.782449e-01 0.0005412932 0.02096420 2.393517e-01
## theta[350] 2.459510e-01 0.0004969506 0.01924681 2.083915e-01
## theta[351] 1.400344e-01 0.0012199939 0.04725016 6.007411e-02
## theta[352] 2.330823e-01 0.0011977780 0.04638974 1.481670e-01
## theta[353] 2.248738e-01 0.0010200082 0.03950475 1.530684e-01
## theta[354] 2.571995e-01 0.0004304843 0.01667259 2.257435e-01
## theta[355] 2.653766e-01 0.0011725934 0.04541435 1.828687e-01
## theta[356] 2.405211e-01 0.0008655858 0.03352399 1.796791e-01
## theta[357] 1.544422e-01 0.0012814521 0.04963043 7.209677e-02
## theta[358] 2.682447e-01 0.0006710145 0.02598828 2.160067e-01
## theta[359] 1.274242e-01 0.0012178397 0.04716673 5.069897e-02
## theta[360] 2.177790e-01 0.0008231710 0.03188128 1.552874e-01
## theta[361] 2.569296e-01 0.0011629836 0.04504216 1.766159e-01
## theta[362] 1.998755e-01 0.0007445388 0.02883586 1.479886e-01
## theta[363] 1.226846e-01 0.0012255297 0.04746456 4.159723e-02
## theta[364] 1.193544e-01 0.0007563180 0.02929207 6.682664e-02
## theta[365] 2.821628e-01 0.0004758123 0.01842813 2.489314e-01
## theta[366] 2.352060e-01 0.0007169615 0.02776780 1.836446e-01
## theta[367] 2.537655e-01 0.0004126213 0.01598076 2.247112e-01
## theta[368] 2.857158e-01 0.0005147501 0.01993619 2.461250e-01
## theta[369] 1.033665e-01 0.0007959471 0.03082690 4.962314e-02
## theta[370] 2.555562e-01 0.0003988686 0.01544811 2.267593e-01
## theta[371] 2.201061e-01 0.0006701660 0.02595542 1.706622e-01
## theta[372] 2.789711e-01 0.0004057769 0.01571567 2.498021e-01
## theta[373] 2.903135e-01 0.0008638441 0.03345654 2.279113e-01
## theta[374] 2.413282e-01 0.0009126003 0.03534486 1.736942e-01
## theta[375] 1.334473e-01 0.0011711054 0.04535672 5.537632e-02
## theta[376] 2.463665e-01 0.0005629845 0.02180430 2.040276e-01
## theta[377] 1.003271e-01 0.0009803290 0.03796798 3.610128e-02
## theta[378] 2.673865e-01 0.0005820035 0.02254090 2.229231e-01
## theta[379] 1.831837e-01 0.0010584931 0.04099526 1.107048e-01
## theta[380] 1.182477e-01 0.0010651082 0.04125146 4.951238e-02
## theta[381] 1.234598e-01 0.0011773778 0.04559965 4.664511e-02
## theta[382] 2.206234e-01 0.0009104809 0.03526277 1.558897e-01
## theta[383] 1.163569e-01 0.0011158854 0.04321806 4.572543e-02
## theta[384] 1.266770e-01 0.0008373731 0.03243132 7.202179e-02
## theta[385] 2.455044e-01 0.0010499170 0.04066311 1.735639e-01
## theta[386] 2.501476e-01 0.0005050026 0.01955867 2.123772e-01
## theta[387] 1.356489e-01 0.0008649885 0.03350086 7.474096e-02
## theta[388] 1.256266e-01 0.0012471440 0.04830168 4.963374e-02
## theta[389] 1.349688e-01 0.0011326115 0.04386586 6.257225e-02
## theta[390] 2.644449e-01 0.0005013297 0.01941642 2.266969e-01
## theta[391] 1.277972e-01 0.0011935775 0.04622706 5.161379e-02
## theta[392] 1.320000e-01 0.0011047395 0.04278638 5.855861e-02
## theta[393] 1.273885e-01 0.0012482584 0.04834484 4.849519e-02
## theta[394] 2.583467e-01 0.0005922306 0.02293699 2.166281e-01
## theta[395] 1.143092e-01 0.0010752717 0.04164509 4.485947e-02
## theta[396] 2.260892e-01 0.0004736453 0.01834421 1.921620e-01
## theta[397] 1.905795e-01 0.0007893595 0.03057176 1.320505e-01
## theta[398] 1.946346e-01 0.0005975212 0.02314190 1.491156e-01
## theta[399] 1.181906e-01 0.0011186005 0.04332321 4.307476e-02
## theta[400] 2.587253e-01 0.0009267949 0.03589461 1.908795e-01
## theta[401] 2.521015e-01 0.0006142355 0.02378924 2.050202e-01
## theta[402] 2.235531e-01 0.0007153093 0.02770381 1.732951e-01
## theta[403] 2.414318e-01 0.0007561392 0.02928515 1.844648e-01
## theta[404] 1.199651e-01 0.0011731381 0.04543544 4.668817e-02
## theta[405] 2.683975e-01 0.0004317662 0.01672223 2.369981e-01
## theta[406] 2.556638e-01 0.0004423190 0.01713094 2.237188e-01
## theta[407] 2.530165e-01 0.0004386864 0.01699025 2.209898e-01
## theta[408] 1.902037e-01 0.0011682310 0.04524539 1.106487e-01
## theta[409] 2.613133e-01 0.0012105494 0.04688438 1.757292e-01
## theta[410] 2.397212e-01 0.0011136446 0.04313127 1.575940e-01
## theta[411] 1.556621e-01 0.0012368094 0.04790142 7.563914e-02
## theta[412] 2.531210e-01 0.0004578843 0.01773378 2.188808e-01
## theta[413] 2.473137e-01 0.0006642150 0.02572494 1.986369e-01
## theta[414] 2.891816e-01 0.0006003598 0.02325184 2.466049e-01
## theta[415] 2.553340e-01 0.0007317406 0.02834019 2.011411e-01
## theta[416] 1.383909e-01 0.0012769507 0.04945609 5.920220e-02
## theta[417] 2.444948e-01 0.0005414774 0.02097133 2.034148e-01
## theta[418] 2.468064e-01 0.0006461286 0.02502445 2.022348e-01
## theta[419] 2.214397e-01 0.0009027162 0.03496205 1.532459e-01
## theta[420] 2.335921e-01 0.0009821172 0.03803723 1.622679e-01
## theta[421] 1.036359e-01 0.0008980764 0.03478235 4.491523e-02
## theta[422] 2.387960e-01 0.0004063837 0.01573917 2.098789e-01
## theta[423] 1.201535e-01 0.0009705991 0.03759114 5.770217e-02
## theta[424] 3.104218e-01 0.0005576356 0.02159714 2.681146e-01
## theta[425] 1.205068e-01 0.0010725150 0.04153833 5.014471e-02
## theta[426] 2.230273e-01 0.0006415503 0.02484714 1.745047e-01
## theta[427] 1.143899e-01 0.0008152633 0.03157501 5.808363e-02
## theta[428] 1.264866e-01 0.0011416086 0.04421431 5.357192e-02
## theta[429] 2.253937e-01 0.0004601451 0.01782134 1.914636e-01
## theta[430] 1.231344e-01 0.0011894960 0.04606898 4.328293e-02
## theta[431] 1.425537e-01 0.0013033656 0.05047913 5.827307e-02
## theta[432] 1.270040e-01 0.0011519907 0.04461641 5.051612e-02
## theta[433] 1.121864e-01 0.0009666048 0.03743644 4.906055e-02
## theta[434] 1.196901e-01 0.0010020553 0.03880943 5.644783e-02
## theta[435] 1.256780e-01 0.0012084080 0.04680144 4.635766e-02
## theta[436] 2.563599e-01 0.0010092472 0.03908798 1.807997e-01
## theta[437] 1.421373e-01 0.0012343501 0.04780617 6.387781e-02
## theta[438] 2.340508e-01 0.0009742037 0.03773075 1.606174e-01
## theta[439] 1.214659e-01 0.0011276678 0.04367439 4.868579e-02
## theta[440] 2.192376e-01 0.0005508722 0.02133519 1.790327e-01
## theta[441] 2.477620e-01 0.0005440428 0.02107069 2.065388e-01
## theta[442] 2.565475e-01 0.0004500293 0.01742956 2.233578e-01
## theta[443] 1.275157e-01 0.0012087425 0.04681440 5.036151e-02
## theta[444] 2.594078e-01 0.0009799598 0.03795368 1.881647e-01
## theta[445] 2.406931e-01 0.0004441206 0.01720072 2.080653e-01
## theta[446] 1.816679e-01 0.0011197886 0.04336923 1.029868e-01
## theta[447] 2.540311e-01 0.0007035276 0.02724751 2.049102e-01
## theta[448] 2.286076e-01 0.0007972521 0.03087744 1.719613e-01
## theta[449] 2.502294e-01 0.0004266955 0.01652585 2.188647e-01
## theta[450] 2.650043e-01 0.0005373663 0.02081211 2.258942e-01
## theta[451] 1.005027e-01 0.0007430094 0.02877663 5.131982e-02
## theta[452] 2.453550e-01 0.0010509706 0.04070392 1.683131e-01
## theta[453] 2.226319e-01 0.0006132934 0.02375275 1.788702e-01
## theta[454] 3.078495e-01 0.0004534579 0.01756235 2.734807e-01
## theta[455] 1.120680e-01 0.0008668194 0.03357177 5.363711e-02
## theta[456] 1.265879e-01 0.0011807256 0.04572931 4.965370e-02
## theta[457] 1.460150e-01 0.0012530828 0.04853169 6.671502e-02
## theta[458] 1.319918e-01 0.0011987180 0.04642615 5.671030e-02
## theta[459] 3.183191e-01 0.0005682727 0.02200911 2.756959e-01
## theta[460] 1.113129e-01 0.0008767347 0.03395579 5.152948e-02
## theta[461] 1.261708e-01 0.0012085621 0.04680741 4.660980e-02
## theta[462] 2.383349e-01 0.0006492094 0.02514377 1.911056e-01
## theta[463] 2.030958e-01 0.0005037635 0.01951068 1.660916e-01
## theta[464] 1.228731e-01 0.0012209523 0.04728728 4.690631e-02
## theta[465] 2.266891e-01 0.0008116143 0.03143369 1.657381e-01
## theta[466] 2.662881e-01 0.0006014623 0.02329453 2.238294e-01
## theta[467] 1.274444e-01 0.0011257838 0.04360142 5.582927e-02
## theta[468] 1.079469e-01 0.0007266467 0.02814291 5.715570e-02
## theta[469] 2.307231e-01 0.0005839463 0.02261614 1.892860e-01
## theta[470] 2.421880e-01 0.0006547426 0.02535807 1.967122e-01
## theta[471] 2.964996e-01 0.0005267512 0.02040099 2.570397e-01
## theta[472] 1.188597e-01 0.0010952866 0.04242027 4.673564e-02
## theta[473] 2.590457e-01 0.0006336601 0.02454155 2.124176e-01
## theta[474] 3.012666e-01 0.0005874861 0.02275324 2.559036e-01
## theta[475] 1.182647e-01 0.0010800836 0.04183146 4.672267e-02
## theta[476] 1.758483e-01 0.0009783099 0.03788978 1.080816e-01
## theta[477] 2.593858e-01 0.0005673951 0.02197512 2.183224e-01
## theta[478] 2.375095e-01 0.0008510028 0.03295920 1.789721e-01
## theta[479] 1.415852e-01 0.0009003177 0.03486915 8.200620e-02
## theta[480] 3.000053e-01 0.0004859859 0.01882215 2.641412e-01
## theta[481] 2.217926e-01 0.0005308853 0.02056110 1.806290e-01
## theta[482] 1.625976e-01 0.0008843580 0.03425104 1.011735e-01
## theta[483] 2.430727e-01 0.0006550156 0.02536865 1.961072e-01
## theta[484] 2.315089e-01 0.0009237184 0.03577546 1.672812e-01
## theta[485] 1.562130e-01 0.0012856724 0.04979388 7.174236e-02
## theta[486] 2.830620e-01 0.0004402838 0.01705212 2.502242e-01
## theta[487] 2.482609e-01 0.0008573283 0.03320418 1.865085e-01
## theta[488] 1.906175e-01 0.0008255352 0.03197284 1.357917e-01
## theta[489] 2.275825e-01 0.0006600639 0.02556417 1.795804e-01
## theta[490] 2.488442e-01 0.0006414393 0.02484284 1.997087e-01
## theta[491] 1.333205e-01 0.0012365154 0.04789004 5.413880e-02
## theta[492] 2.287856e-01 0.0005954193 0.02306049 1.843905e-01
## theta[493] 1.236329e-01 0.0011852677 0.04590522 4.648814e-02
## theta[494] 2.472421e-01 0.0005253321 0.02034602 2.076271e-01
## theta[495] 1.069247e-01 0.0009517699 0.03686189 4.674868e-02
## theta[496] 1.143687e-01 0.0010488066 0.04062010 4.663128e-02
## theta[497] 2.450754e-01 0.0005602501 0.02169839 2.048503e-01
## theta[498] 2.816866e-01 0.0004810970 0.01863281 2.470651e-01
## theta[499] 2.384577e-01 0.0006069945 0.02350880 1.950528e-01
## theta[500] 1.123189e-01 0.0007403504 0.02867365 6.376064e-02
## theta[501] 1.209009e-01 0.0010761898 0.04168065 5.167156e-02
## theta[502] 2.440810e-01 0.0004342274 0.01681755 2.120719e-01
## theta[503] 1.201100e-01 0.0010627587 0.04116047 4.803208e-02
## theta[504] 2.677111e-01 0.0005876242 0.02275859 2.245276e-01
## theta[505] 1.272549e-01 0.0012045182 0.04665079 4.958528e-02
## theta[506] 2.338203e-01 0.0005265830 0.02039447 1.930954e-01
## theta[507] 1.527935e-01 0.0012643789 0.04896918 7.005120e-02
## theta[508] 1.857265e-01 0.0007377101 0.02857139 1.322423e-01
## theta[509] 2.586375e-01 0.0004570197 0.01770030 2.232273e-01
## theta[510] 2.433591e-01 0.0006523993 0.02526732 1.945816e-01
## theta[511] 1.259902e-01 0.0010511005 0.04070895 5.754714e-02
## theta[512] 2.936356e-01 0.0005482019 0.02123177 2.511810e-01
## theta[513] 2.461961e-01 0.0005640911 0.02184715 2.024191e-01
## theta[514] 2.174449e-01 0.0006825764 0.02643607 1.675517e-01
## theta[515] 1.241519e-01 0.0012025690 0.04657530 4.846839e-02
## theta[516] 2.381658e-01 0.0009776090 0.03786263 1.687320e-01
## theta[517] 2.044652e-01 0.0008830944 0.03420210 1.394307e-01
## theta[518] 1.120520e-01 0.0010049203 0.03892040 4.765496e-02
## theta[519] 1.261722e-01 0.0011690557 0.04527733 5.361608e-02
## theta[520] 1.285779e-01 0.0012230948 0.04737026 5.039030e-02
## theta[521] 2.359544e-01 0.0005347072 0.02070912 1.964469e-01
## theta[522] 2.643963e-01 0.0004503396 0.01744158 2.327512e-01
## theta[523] 2.995378e-01 0.0006146622 0.02380577 2.548909e-01
## theta[524] 2.309286e-01 0.0009819908 0.03803234 1.635363e-01
## theta[525] 2.234953e-01 0.0004433906 0.01717244 1.918237e-01
## theta[526] 2.625403e-01 0.0007117952 0.02756771 2.109428e-01
## theta[527] 2.760142e-01 0.0004395565 0.01702395 2.440820e-01
## theta[528] 1.203499e-01 0.0011488318 0.04449406 4.699625e-02
## theta[529] 2.287353e-01 0.0004172439 0.01615979 1.969868e-01
## theta[530] 2.353507e-01 0.0006203151 0.02402470 1.899135e-01
## theta[531] 2.691516e-01 0.0004599797 0.01781494 2.358576e-01
## theta[532] 1.269684e-01 0.0012894721 0.04994104 4.656309e-02
## theta[533] 1.180435e-01 0.0008878510 0.03438632 5.804055e-02
## theta[534] 3.104776e-01 0.0007063052 0.02735508 2.569109e-01
## theta[535] 2.341604e-01 0.0010337419 0.04003665 1.587412e-01
## theta[536] 1.196335e-01 0.0011450596 0.04434797 4.524370e-02
## theta[537] 2.389459e-01 0.0004606617 0.01784135 2.051221e-01
## theta[538] 1.189898e-01 0.0010217673 0.03957288 5.356419e-02
## theta[539] 2.542376e-01 0.0005988102 0.02319182 2.100675e-01
## theta[540] 2.442574e-01 0.0010102234 0.03912578 1.701904e-01
## theta[541] 2.248079e-01 0.0010878736 0.04213316 1.465704e-01
## theta[542] 2.261713e-01 0.0009058541 0.03508358 1.586437e-01
## theta[543] 2.190780e-01 0.0009471727 0.03668384 1.522029e-01
## theta[544] 1.256045e-01 0.0009458807 0.03663380 6.189213e-02
## theta[545] 2.575397e-01 0.0012028833 0.04658747 1.723398e-01
## theta[546] 2.358490e-01 0.0004857015 0.01881114 2.004835e-01
## theta[547] 2.546100e-01 0.0010933336 0.04234463 1.785342e-01
## theta[548] 1.236271e-01 0.0012120719 0.04694334 4.697029e-02
## theta[549] 1.327780e-01 0.0009424509 0.03650097 7.093056e-02
## theta[550] 1.089732e-01 0.0007376344 0.02856846 5.844352e-02
## theta[551] 1.268208e-01 0.0012475020 0.04831555 4.730997e-02
## theta[552] 1.159154e-01 0.0011001243 0.04260763 4.576288e-02
## theta[553] 2.593122e-01 0.0004235864 0.01640543 2.283545e-01
## theta[554] 1.147097e-01 0.0011168376 0.04325494 4.203230e-02
## theta[555] 2.561093e-01 0.0008883704 0.03440644 1.927682e-01
## theta[556] 9.865054e-02 0.0007768794 0.03008841 4.673849e-02
## theta[557] 2.382635e-01 0.0010481932 0.04059635 1.645235e-01
## theta[558] 2.481652e-01 0.0007139693 0.02765191 1.928678e-01
## theta[559] 2.299438e-01 0.0009696102 0.03755284 1.609228e-01
## theta[560] 2.220043e-01 0.0008027951 0.03109212 1.639442e-01
## theta[561] 1.239458e-01 0.0012215986 0.04731231 4.287743e-02
## theta[562] 1.244187e-01 0.0011473868 0.04443810 5.007011e-02
## theta[563] 2.666669e-01 0.0005373907 0.02081305 2.263934e-01
## theta[564] 2.365360e-01 0.0005431268 0.02103521 1.960117e-01
## theta[565] 2.676659e-01 0.0011255696 0.04359312 1.902072e-01
## theta[566] 2.598499e-01 0.0007289250 0.02823114 2.050387e-01
## theta[567] 2.632228e-01 0.0006244747 0.02418580 2.158483e-01
## theta[568] 2.284270e-01 0.0006419280 0.02486176 1.815216e-01
## theta[569] 2.440729e-01 0.0005006508 0.01939012 2.081042e-01
## theta[570] 1.417224e-01 0.0008446761 0.03271416 8.586537e-02
## theta[571] 1.433250e-01 0.0012839561 0.04972741 6.261560e-02
## theta[572] 2.869114e-01 0.0006045331 0.02341347 2.421218e-01
## theta[573] 2.047781e-01 0.0009897528 0.03833296 1.335143e-01
## theta[574] 2.497367e-01 0.0011222475 0.04346446 1.670683e-01
## theta[575] 1.264302e-01 0.0011751698 0.04551413 5.113048e-02
## theta[576] 1.294878e-01 0.0012082429 0.04679504 5.152826e-02
## theta[577] 2.297008e-01 0.0005990475 0.02320101 1.858676e-01
## theta[578] 2.325201e-01 0.0010798678 0.04182310 1.544329e-01
## theta[579] 1.257781e-01 0.0011847714 0.04588600 5.312808e-02
## theta[580] 1.356714e-01 0.0011694621 0.04529307 5.714399e-02
## theta[581] 2.306533e-01 0.0010046742 0.03891086 1.560298e-01
## theta[582] 2.361714e-01 0.0005405529 0.02093552 1.952059e-01
## theta[583] 2.574195e-01 0.0007535152 0.02918352 2.024819e-01
## theta[584] 1.493853e-01 0.0008615827 0.03336896 8.961009e-02
## theta[585] 2.551195e-01 0.0005877766 0.02276449 2.086339e-01
## theta[586] 1.295885e-01 0.0012413763 0.04807830 4.804112e-02
## theta[587] 2.577920e-01 0.0006432963 0.02491476 2.123574e-01
## theta[588] 1.255817e-01 0.0012004404 0.04649286 4.951775e-02
## theta[589] 2.328262e-01 0.0011596734 0.04491396 1.525499e-01
## theta[590] 1.152732e-01 0.0008383732 0.03247005 5.783495e-02
## theta[591] 2.980655e-01 0.0004183125 0.01620117 2.657920e-01
## theta[592] 8.342716e-02 0.0006668357 0.02582643 3.964222e-02
## theta[593] 2.246644e-01 0.0008438034 0.03268036 1.618026e-01
## theta[594] 2.555125e-01 0.0004790333 0.01855288 2.195939e-01
## theta[595] 2.558295e-01 0.0007070004 0.02738201 2.044563e-01
## theta[596] 2.267814e-01 0.0004496746 0.01741582 1.936022e-01
## theta[597] 1.509674e-01 0.0011683977 0.04525185 7.366538e-02
## theta[598] 2.515755e-01 0.0004907063 0.01900497 2.148815e-01
## theta[599] 2.647072e-01 0.0004396217 0.01702648 2.313391e-01
## theta[600] 2.315569e-01 0.0007365139 0.02852506 1.777400e-01
## theta[601] 2.592080e-01 0.0006710450 0.02598946 2.088341e-01
## theta[602] 2.937179e-01 0.0004420720 0.01712137 2.622813e-01
## theta[603] 2.377229e-01 0.0006295007 0.02438046 1.910654e-01
## theta[604] 2.501322e-01 0.0008490929 0.03288523 1.898309e-01
## theta[605] 1.611387e-01 0.0008506727 0.03294641 1.009436e-01
## theta[606] 2.523344e-01 0.0007904703 0.03061478 1.959769e-01
## theta[607] 1.235758e-01 0.0011559384 0.04476930 4.998035e-02
## theta[608] 1.579714e-01 0.0008426252 0.03263473 1.006191e-01
## theta[609] 2.819523e-01 0.0005703806 0.02209074 2.396148e-01
## theta[610] 2.396362e-01 0.0008265955 0.03201390 1.785377e-01
## theta[611] 2.363380e-01 0.0007616260 0.02949765 1.785138e-01
## theta[612] 2.716975e-01 0.0008373356 0.03242987 2.080277e-01
## theta[613] 2.182584e-01 0.0006504076 0.02519018 1.684969e-01
## theta[614] 1.054461e-01 0.0008881031 0.03439608 4.979441e-02
## theta[615] 2.429381e-01 0.0008620086 0.03338545 1.818702e-01
## theta[616] 1.198723e-01 0.0010894431 0.04219395 4.987171e-02
## theta[617] 1.826643e-01 0.0012594489 0.04877824 1.031073e-01
## theta[618] 2.891335e-01 0.0004532319 0.01755359 2.551980e-01
## theta[619] 2.935935e-01 0.0005634720 0.02182318 2.538171e-01
## theta[620] 2.482595e-01 0.0009070657 0.03513050 1.842446e-01
## theta[621] 2.341250e-01 0.0008007457 0.03101275 1.753924e-01
## theta[622] 1.189849e-01 0.0011216958 0.04344309 4.800648e-02
## theta[623] 2.035437e-01 0.0007551469 0.02924671 1.467305e-01
## theta[624] 2.478921e-01 0.0004786119 0.01853656 2.115087e-01
## theta[625] 2.436516e-01 0.0004787414 0.01854157 2.075326e-01
## theta[626] 2.644217e-01 0.0007865263 0.03046203 2.080711e-01
## theta[627] 1.245492e-01 0.0011993427 0.04645034 4.684954e-02
## theta[628] 3.287110e-01 0.0005240030 0.02029455 2.890187e-01
## theta[629] 2.618473e-01 0.0011653715 0.04513465 1.812985e-01
## theta[630] 1.238470e-01 0.0011649478 0.04511823 4.866934e-02
## theta[631] 2.714623e-01 0.0004424224 0.01713495 2.368175e-01
## theta[632] 1.238042e-01 0.0011582803 0.04486000 5.148722e-02
## theta[633] 2.831520e-01 0.0004528737 0.01753972 2.497010e-01
## theta[634] 2.596852e-01 0.0005379043 0.02083294 2.168758e-01
## theta[635] 2.092682e-01 0.0006957970 0.02694810 1.599361e-01
## theta[636] 2.344156e-01 0.0006058878 0.02346593 1.900176e-01
## theta[637] 2.485269e-01 0.0004340434 0.01681043 2.161920e-01
## theta[638] 2.720685e-01 0.0004294247 0.01663155 2.393453e-01
## theta[639] 1.157824e-01 0.0010346193 0.04007063 4.790116e-02
## theta[640] 3.206482e-01 0.0004471453 0.01731786 2.880665e-01
## theta[641] 2.146456e-01 0.0006429205 0.02490021 1.664288e-01
## theta[642] 2.778915e-01 0.0004944101 0.01914842 2.410617e-01
## theta[643] 2.271695e-01 0.0005421948 0.02099911 1.875160e-01
## theta[644] 2.504719e-01 0.0004783041 0.01852464 2.144915e-01
## theta[645] 2.610255e-01 0.0006852120 0.02653815 2.120896e-01
## theta[646] 2.277793e-01 0.0006842076 0.02649925 1.796271e-01
## theta[647] 2.224126e-01 0.0010008023 0.03876091 1.484165e-01
## theta[648] 1.282285e-01 0.0012334746 0.04777226 5.102783e-02
## theta[649] 1.153598e-01 0.0009128590 0.03535488 5.159563e-02
## theta[650] 2.670454e-01 0.0008216726 0.03182324 2.078426e-01
## theta[651] 2.195937e-01 0.0010539274 0.04081843 1.485516e-01
## theta[652] 1.261617e-01 0.0012039434 0.04662853 4.936447e-02
## theta[653] 2.220345e-01 0.0009420750 0.03648641 1.516045e-01
## theta[654] 9.984297e-02 0.0007799550 0.03020753 5.011216e-02
## theta[655] 2.829146e-01 0.0004963643 0.01922411 2.461074e-01
## theta[656] 2.437858e-01 0.0004477283 0.01734044 2.100920e-01
## theta[657] 2.294680e-01 0.0005135809 0.01989090 1.903391e-01
## theta[658] 2.023836e-01 0.0007664260 0.02968355 1.460227e-01
## theta[659] 2.259989e-01 0.0009654188 0.03739051 1.574645e-01
## theta[660] 1.326376e-01 0.0011643494 0.04509506 5.549417e-02
## theta[661] 3.162649e-01 0.0004753663 0.01841086 2.807891e-01
## theta[662] 1.221671e-01 0.0011599512 0.04492472 4.699433e-02
## theta[663] 2.221728e-01 0.0008299006 0.03214191 1.628841e-01
## theta[664] 2.704327e-01 0.0005548005 0.02148733 2.294945e-01
## theta[665] 2.391736e-01 0.0007385582 0.02860424 1.846962e-01
## theta[666] 2.162069e-01 0.0008003350 0.03099684 1.580150e-01
## theta[667] 2.424989e-01 0.0005791685 0.02243110 1.996823e-01
## theta[668] 2.577877e-01 0.0006067088 0.02349773 2.120873e-01
## theta[669] 2.348362e-01 0.0010663923 0.04130120 1.587994e-01
## theta[670] 1.280406e-01 0.0011648587 0.04511478 5.077962e-02
## theta[671] 1.162706e-01 0.0008993848 0.03483302 5.661408e-02
## theta[672] 1.268794e-01 0.0012184793 0.04719150 5.204692e-02
## theta[673] 2.745618e-01 0.0004751088 0.01840088 2.385645e-01
## theta[674] 1.274232e-01 0.0012559082 0.04864112 4.933766e-02
## theta[675] 2.383837e-01 0.0010587251 0.04100425 1.622648e-01
## theta[676] 1.814293e-01 0.0005855148 0.02267689 1.386568e-01
## theta[677] 2.329232e-01 0.0008221981 0.03184360 1.738622e-01
## theta[678] 2.904315e-01 0.0004825295 0.01868829 2.531218e-01
## theta[679] 2.324474e-01 0.0007032926 0.02723841 1.814608e-01
## theta[680] 2.694521e-01 0.0004638446 0.01796463 2.347490e-01
## theta[681] 1.281939e-01 0.0012546675 0.04859306 4.966846e-02
## theta[682] 2.730109e-01 0.0009359079 0.03624756 2.057253e-01
## theta[683] 2.427365e-01 0.0005706066 0.02209950 2.006357e-01
## theta[684] 2.703191e-01 0.0004491254 0.01739455 2.375633e-01
## theta[685] 2.456737e-01 0.0006564953 0.02542595 1.977605e-01
## theta[686] 2.405470e-01 0.0006694875 0.02592914 1.924876e-01
## theta[687] 2.286962e-01 0.0011220558 0.04345704 1.487985e-01
## theta[688] 2.165264e-01 0.0005899537 0.02284881 1.753618e-01
## theta[689] 2.794578e-01 0.0004987426 0.01931622 2.430919e-01
## theta[690] 1.215855e-01 0.0009319292 0.03609346 6.120633e-02
## theta[691] 2.800854e-01 0.0004544401 0.01760039 2.467083e-01
## theta[692] 2.065424e-01 0.0006641465 0.02572228 1.589090e-01
## theta[693] 2.914850e-01 0.0004598329 0.01780925 2.573941e-01
## theta[694] 9.558384e-02 0.0007021473 0.02719405 4.955333e-02
## theta[695] 2.464023e-01 0.0004506664 0.01745423 2.126359e-01
## theta[696] 2.815175e-01 0.0005918601 0.02292264 2.376424e-01
## theta[697] 2.297323e-01 0.0007174981 0.02778858 1.791497e-01
## theta[698] 2.865762e-01 0.0009252988 0.03583667 2.208989e-01
## theta[699] 2.714260e-01 0.0008847789 0.03426734 2.059312e-01
## theta[700] 2.318385e-01 0.0006704402 0.02596604 1.829281e-01
## theta[701] 1.260655e-01 0.0011804404 0.04571826 5.214786e-02
## theta[702] 1.350460e-01 0.0011897040 0.04607704 5.699821e-02
## theta[703] 2.566115e-01 0.0005210029 0.02017836 2.172184e-01
## theta[704] 3.058993e-01 0.0004700942 0.01820667 2.702686e-01
## theta[705] 2.548364e-01 0.0005364642 0.02077717 2.155376e-01
## theta[706] 2.622286e-01 0.0004643885 0.01798569 2.278600e-01
## theta[707] 2.627026e-01 0.0011745191 0.04548893 1.800455e-01
## theta[708] 2.551772e-01 0.0004920463 0.01905687 2.185460e-01
## theta[709] 2.499569e-01 0.0011578263 0.04484242 1.682826e-01
## theta[710] 2.190007e-01 0.0005879019 0.02276934 1.771334e-01
## theta[711] 1.663231e-01 0.0011557923 0.04476364 9.161267e-02
## theta[712] 1.385203e-01 0.0011783377 0.04563682 6.401047e-02
## theta[713] 1.384251e-01 0.0009493223 0.03676710 7.513272e-02
## theta[714] 2.422578e-01 0.0005050285 0.01955967 2.052024e-01
## theta[715] 2.482482e-01 0.0009245752 0.03580864 1.833641e-01
## theta[716] 2.780519e-01 0.0005621002 0.02177005 2.360460e-01
## theta[717] 2.174918e-01 0.0010920317 0.04229420 1.371405e-01
## theta[718] 1.250934e-01 0.0011686520 0.04526170 5.049942e-02
## theta[719] 1.272601e-01 0.0012577245 0.04871146 4.873523e-02
## theta[720] 2.391978e-01 0.0007347607 0.02845716 1.870007e-01
## theta[721] 1.221093e-01 0.0011921028 0.04616994 4.535581e-02
## theta[722] 2.332330e-01 0.0003911966 0.01515098 2.044654e-01
## theta[723] 1.472298e-01 0.0008843636 0.03425125 8.461294e-02
## theta[724] 1.349749e-01 0.0012297298 0.04762723 5.796171e-02
## theta[725] 2.634889e-01 0.0008214214 0.03181351 2.059045e-01
## theta[726] 2.429231e-01 0.0009264049 0.03587951 1.759676e-01
## theta[727] 1.283211e-01 0.0011236786 0.04351988 5.546796e-02
## theta[728] 1.249490e-01 0.0011515318 0.04459863 4.968499e-02
## theta[729] 2.190758e-01 0.0004642721 0.01798118 1.851256e-01
## theta[730] 3.042624e-01 0.0004445560 0.01721758 2.709614e-01
## theta[731] 2.143584e-01 0.0005188945 0.02009670 1.758259e-01
## theta[732] 2.767735e-01 0.0006671035 0.02583681 2.266920e-01
## theta[733] 1.300272e-01 0.0012536399 0.04855327 5.203737e-02
## theta[734] 2.556812e-01 0.0006706287 0.02597334 2.072011e-01
## theta[735] 2.469844e-01 0.0009038906 0.03500753 1.834068e-01
## theta[736] 8.946748e-02 0.0007671973 0.02971342 4.116811e-02
## theta[737] 1.147749e-01 0.0010000512 0.03873182 5.305969e-02
## theta[738] 1.495192e-01 0.0009200634 0.03563390 8.808301e-02
## theta[739] 2.822143e-01 0.0004871351 0.01886666 2.468986e-01
## theta[740] 2.584886e-01 0.0008126193 0.03147261 2.000705e-01
## theta[741] 2.154153e-01 0.0004529492 0.01754265 1.814981e-01
## theta[742] 1.159051e-01 0.0008828967 0.03419444 5.526614e-02
## theta[743] 2.691766e-01 0.0004846046 0.01876866 2.343116e-01
## theta[744] 2.310597e-01 0.0006839863 0.02649068 1.811116e-01
## theta[745] 2.667274e-01 0.0005537385 0.02144620 2.262893e-01
## theta[746] 2.296261e-01 0.0005856837 0.02268343 1.880120e-01
## theta[747] 2.442088e-01 0.0007782573 0.03014177 1.858439e-01
## theta[748] 2.464053e-01 0.0011457032 0.04437289 1.628874e-01
## theta[749] 1.877948e-01 0.0006512215 0.02522170 1.385774e-01
## theta[750] 2.699648e-01 0.0004868550 0.01885581 2.326855e-01
## theta[751] 1.281488e-01 0.0012102390 0.04687235 5.210511e-02
## theta[752] 1.972257e-01 0.0005877597 0.02276384 1.550021e-01
## theta[753] 2.377421e-01 0.0004913198 0.01902873 1.993282e-01
## theta[754] 2.602366e-01 0.0006733673 0.02607940 2.116239e-01
## theta[755] 2.653250e-01 0.0005573700 0.02158685 2.252672e-01
## theta[756] 1.116720e-01 0.0008379075 0.03245202 5.516006e-02
## theta[757] 1.288596e-01 0.0012226050 0.04735129 4.950334e-02
## theta[758] 2.474641e-01 0.0008000717 0.03098665 1.875886e-01
## theta[759] 2.788848e-01 0.0004544479 0.01760069 2.440814e-01
## theta[760] 2.869949e-01 0.0006261900 0.02425223 2.418596e-01
## theta[761] 2.558669e-01 0.0007914515 0.03065279 1.973325e-01
## theta[762] 1.287173e-01 0.0011714513 0.04537012 5.127428e-02
## theta[763] 2.489897e-01 0.0010062051 0.03897016 1.787321e-01
## theta[764] 1.422384e-01 0.0011556919 0.04475976 6.619697e-02
## theta[765] 2.118437e-01 0.0008291163 0.03211154 1.503923e-01
## theta[766] 1.301987e-01 0.0011630274 0.04504386 5.588973e-02
## theta[767] 1.358866e-01 0.0012053009 0.04668110 5.736843e-02
## theta[768] 2.597458e-01 0.0004942203 0.01914107 2.221662e-01
## theta[769] 1.254490e-01 0.0011588988 0.04488396 4.943940e-02
## theta[770] 2.571655e-01 0.0006388413 0.02474222 2.101036e-01
## theta[771] 2.804955e-01 0.0006648916 0.02575114 2.297396e-01
## theta[772] 2.478845e-01 0.0005731836 0.02219930 2.071693e-01
## theta[773] 2.267681e-01 0.0008979815 0.03477867 1.606722e-01
## theta[774] 2.333682e-01 0.0010754858 0.04165338 1.560876e-01
## theta[775] 2.229938e-01 0.0005400775 0.02091711 1.832534e-01
## theta[776] 2.417020e-01 0.0005030574 0.01948333 2.063006e-01
## theta[777] 1.292795e-01 0.0013103703 0.05075042 4.551162e-02
## theta[778] 2.530798e-01 0.0007302704 0.02828325 1.989202e-01
## theta[779] 2.559480e-01 0.0004416202 0.01710387 2.228062e-01
## theta[780] 1.188594e-01 0.0009103056 0.03525598 6.046158e-02
## theta[781] 1.624755e-01 0.0013706252 0.05308409 7.475311e-02
## theta[782] 2.173753e-01 0.0005542118 0.02146453 1.729704e-01
## theta[783] 2.682127e-01 0.0005945176 0.02302557 2.236525e-01
## theta[784] 2.795842e-01 0.0004394846 0.01702116 2.463967e-01
## theta[785] 2.538511e-01 0.0007008572 0.02714408 2.018762e-01
## theta[786] 2.296505e-01 0.0005860382 0.02269716 1.884097e-01
## theta[787] 1.497059e-01 0.0012246058 0.04742878 7.478963e-02
## theta[788] 2.011798e-01 0.0010861316 0.04206569 1.285890e-01
## theta[789] 1.864342e-01 0.0009346884 0.03620033 1.219413e-01
## theta[790] 1.269173e-01 0.0011843162 0.04586837 5.348768e-02
## theta[791] 2.126390e-01 0.0006233333 0.02414160 1.668741e-01
## theta[792] 1.267163e-01 0.0011805541 0.04572266 4.970487e-02
## theta[793] 2.432143e-01 0.0006490559 0.02513783 1.968342e-01
## theta[794] 2.472360e-01 0.0010460885 0.04051483 1.713632e-01
## theta[795] 2.355448e-01 0.0010866739 0.04208670 1.591755e-01
## theta[796] 2.214950e-01 0.0009251292 0.03583010 1.561121e-01
## theta[797] 2.170161e-01 0.0007667535 0.02969623 1.605773e-01
## theta[798] 2.069629e-01 0.0009071232 0.03513273 1.415535e-01
## theta[799] 1.147623e-01 0.0010959177 0.04244471 4.560558e-02
## theta[800] 2.445182e-01 0.0011239249 0.04352942 1.638799e-01
## theta[801] 2.448681e-01 0.0009555632 0.03700880 1.723244e-01
## theta[802] 1.263682e-01 0.0012335314 0.04777447 5.110193e-02
## theta[803] 2.437844e-01 0.0011986484 0.04642345 1.623255e-01
## theta[804] 1.738594e-01 0.0009271042 0.03590659 1.081810e-01
## theta[805] 1.086414e-01 0.0007964052 0.03084464 5.390822e-02
## theta[806] 1.295221e-01 0.0012221278 0.04733281 5.156415e-02
## theta[807] 2.694430e-01 0.0004865899 0.01884555 2.339549e-01
## theta[808] 2.418499e-01 0.0005534497 0.02143502 1.987210e-01
## theta[809] 1.277860e-01 0.0011517579 0.04460739 4.843963e-02
## theta[810] 1.530008e-01 0.0012721550 0.04927035 6.925178e-02
## theta[811] 1.294902e-01 0.0012620827 0.04888025 4.924667e-02
## theta[812] 7.517419e-02 0.0007119223 0.02757263 3.081216e-02
## theta[813] 1.279015e-01 0.0012720121 0.04926482 5.156983e-02
## theta[814] 1.376791e-01 0.0011600622 0.04492901 6.362014e-02
## theta[815] 2.546008e-01 0.0009232547 0.03575750 1.870302e-01
## theta[816] 2.616366e-01 0.0006951892 0.02692456 2.091529e-01
## theta[817] 1.261731e-01 0.0012038430 0.04662464 4.722269e-02
## theta[818] 2.476414e-01 0.0007451048 0.02885778 1.920907e-01
## theta[819] 1.286095e-01 0.0012151062 0.04706086 5.036186e-02
## theta[820] 3.033125e-01 0.0004901954 0.01898519 2.656556e-01
## theta[821] 1.223072e-01 0.0011842741 0.04586674 4.495575e-02
## theta[822] 2.364038e-01 0.0008169286 0.03163951 1.769292e-01
## theta[823] 2.539290e-01 0.0007162694 0.02774099 2.022932e-01
## theta[824] 2.556032e-01 0.0006986896 0.02706013 2.049411e-01
## theta[825] 1.578728e-01 0.0009091550 0.03521142 9.852016e-02
## theta[826] 2.327372e-01 0.0006796260 0.02632180 1.842940e-01
## theta[827] 1.204328e-01 0.0011019934 0.04268002 5.030959e-02
## theta[828] 1.244107e-01 0.0007585437 0.02937827 7.152985e-02
## theta[829] 2.377417e-01 0.0004834308 0.01872319 2.020912e-01
## theta[830] 2.734354e-01 0.0007220712 0.02796570 2.212577e-01
## theta[831] 2.182153e-01 0.0009924208 0.03843629 1.481058e-01
## theta[832] 2.391549e-01 0.0005446808 0.02109540 1.986399e-01
## theta[833] 1.570396e-01 0.0011366437 0.04402202 8.470134e-02
## theta[834] 1.218541e-01 0.0011302424 0.04377410 4.840916e-02
## theta[835] 2.832756e-01 0.0005223362 0.02022999 2.459052e-01
## theta[836] 2.250726e-01 0.0007331162 0.02839347 1.726860e-01
## theta[837] 2.499981e-01 0.0012285938 0.04758323 1.618454e-01
## theta[838] 2.339222e-01 0.0005335319 0.02066360 1.934146e-01
## theta[839] 2.570526e-01 0.0006836560 0.02647788 2.070313e-01
## theta[840] 2.438248e-01 0.0006667519 0.02582319 1.932926e-01
## theta[841] 1.123632e-01 0.0010676471 0.04134979 4.334033e-02
## theta[842] 1.359359e-01 0.0011988174 0.04643000 5.780368e-02
## theta[843] 1.268049e-01 0.0012283441 0.04757356 5.039067e-02
## theta[844] 1.162458e-01 0.0011262353 0.04361891 4.027724e-02
## theta[845] 1.121244e-01 0.0008441107 0.03269227 5.400888e-02
## theta[846] 2.363109e-01 0.0006171789 0.02390324 1.921056e-01
## theta[847] 1.287992e-01 0.0012670400 0.04907225 4.643193e-02
## theta[848] 1.583211e-01 0.0013170977 0.05101097 7.279994e-02
## theta[849] 2.110891e-01 0.0008331273 0.03226688 1.521646e-01
## theta[850] 1.428890e-01 0.0012510225 0.04845189 5.798119e-02
## theta[851] 1.202278e-01 0.0010562694 0.04090914 5.062930e-02
## theta[852] 1.518060e-01 0.0008641429 0.03346811 9.293311e-02
## theta[853] 9.445579e-02 0.0006874462 0.02662468 4.861407e-02
## theta[854] 2.557738e-01 0.0007010604 0.02715195 2.056524e-01
## theta[855] 1.241701e-01 0.0011786754 0.04564990 5.005569e-02
## theta[856] 2.652678e-01 0.0008626193 0.03340910 2.023826e-01
## theta[857] 2.644117e-01 0.0004912979 0.01902789 2.287796e-01
## theta[858] 2.792723e-01 0.0005964010 0.02309851 2.354788e-01
## theta[859] 2.369174e-01 0.0007449601 0.02885218 1.824209e-01
## theta[860] 2.616455e-01 0.0004694425 0.01818143 2.289442e-01
## theta[861] 2.910004e-01 0.0005950429 0.02304591 2.484803e-01
## theta[862] 2.092653e-01 0.0008964665 0.03472000 1.404360e-01
## theta[863] 2.599789e-01 0.0005667713 0.02195096 2.189347e-01
## theta[864] 2.552624e-01 0.0008555726 0.03313619 1.939701e-01
## theta[865] 2.179587e-01 0.0006181229 0.02393980 1.703738e-01
## theta[866] 1.269273e-01 0.0011035039 0.04273852 5.238706e-02
## theta[867] 2.364385e-01 0.0007947423 0.03078024 1.786439e-01
## theta[868] 1.271850e-01 0.0012352616 0.04784148 5.260708e-02
## theta[869] 2.111403e-01 0.0006622105 0.02564730 1.642497e-01
## theta[870] 2.780166e-01 0.0008540736 0.03307813 2.179635e-01
## theta[871] 3.028907e-01 0.0004575249 0.01771986 2.689810e-01
## theta[872] 2.214076e-01 0.0008327320 0.03225157 1.595531e-01
## theta[873] 2.272892e-01 0.0007840828 0.03036740 1.723916e-01
## theta[874] 2.794732e-01 0.0006367499 0.02466122 2.325083e-01
## theta[875] 2.848681e-01 0.0004916665 0.01904216 2.477244e-01
## theta[876] 2.695397e-01 0.0004464578 0.01729124 2.368252e-01
## theta[877] 2.299971e-01 0.0006634258 0.02569437 1.818662e-01
## theta[878] 1.482898e-01 0.0008175853 0.03166494 9.279913e-02
## theta[879] 1.422732e-01 0.0012689341 0.04914560 5.950192e-02
## theta[880] 2.528679e-01 0.0004540673 0.01758595 2.188944e-01
## theta[881] 2.355398e-01 0.0005999558 0.02323619 1.902326e-01
## theta[882] 1.339579e-01 0.0012351843 0.04783848 5.271825e-02
## theta[883] 1.263450e-01 0.0011518175 0.04460970 5.252297e-02
## theta[884] 2.378513e-01 0.0010477802 0.04058035 1.648485e-01
## theta[885] 2.461841e-01 0.0004120959 0.01596041 2.156898e-01
## theta[886] 1.618195e-01 0.0010508510 0.04069928 9.157926e-02
## gamma[1] -1.091905e+00 0.0008745969 0.03387299 -1.158386e+00
## gamma[2] -1.094799e+00 0.0010084576 0.03905739 -1.177104e+00
## gamma[3] -1.069246e+00 0.0008913752 0.03452281 -1.138531e+00
## gamma[4] -1.169225e+00 0.0009543842 0.03696314 -1.243501e+00
## gamma[5] -1.051255e+00 0.0010109287 0.03915310 -1.128573e+00
## gamma[6] -1.105599e+00 0.0007842691 0.03037461 -1.166049e+00
## gamma[7] -1.903222e+00 0.0027388346 0.05657094 -2.020178e+00
## gamma[8] -1.056253e+00 0.0009778936 0.03787366 -1.131003e+00
## gamma[9] -1.102987e+00 0.0010931238 0.04233650 -1.188763e+00
## alpha_w 1.958130e-02 0.0005435595 0.01750731 -1.363324e-02
## alpha_h -9.207362e-03 0.0006168918 0.01717738 -4.178603e-02
## kappa[1] 1.077079e+02 0.7262494175 22.65586834 6.772902e+01
## kappa[2] 1.052507e+02 0.6033494199 23.36762255 6.680898e+01
## kappa[3] 9.662457e+01 0.5583136902 21.62339624 6.154558e+01
## kappa[4] 9.140203e+01 0.6524148542 18.98007251 5.765711e+01
## kappa[5] 9.333947e+01 0.5950655606 23.04679006 5.408878e+01
## kappa[6] 1.073024e+02 0.7788499531 22.65824110 7.008991e+01
## kappa[7] 5.283281e+01 1.3038785428 13.98002066 3.110344e+01
## kappa[8] 1.090504e+02 0.6945457622 26.89964170 6.438303e+01
## kappa[9] 8.984522e+01 0.5885281244 22.79359625 5.071070e+01
## lp__ -8.740591e+04 3.6647296522 40.36019424 -8.748964e+04
## 25% 50% 75% 97.5%
## theta[1] 1.949831e-01 2.132776e-01 2.332172e-01 2.743765e-01
## theta[2] 8.015649e-02 9.771761e-02 1.166936e-01 1.611140e-01
## theta[3] 2.828673e-01 2.939698e-01 3.056620e-01 3.275891e-01
## theta[4] 9.191019e-02 1.193606e-01 1.520419e-01 2.316591e-01
## theta[5] 9.233393e-02 1.230127e-01 1.562750e-01 2.358290e-01
## theta[6] 2.023921e-01 2.128437e-01 2.231732e-01 2.469481e-01
## theta[7] 2.723701e-01 2.830544e-01 2.945211e-01 3.178243e-01
## theta[8] 2.400461e-01 2.586267e-01 2.777600e-01 3.173837e-01
## theta[9] 2.558001e-01 2.675199e-01 2.793480e-01 3.026482e-01
## theta[10] 2.395704e-01 2.535546e-01 2.671032e-01 2.927895e-01
## theta[11] 2.027348e-01 2.283763e-01 2.558034e-01 3.176946e-01
## theta[12] 9.529698e-02 1.235268e-01 1.537204e-01 2.185064e-01
## theta[13] 2.142402e-01 2.341442e-01 2.561176e-01 2.980533e-01
## theta[14] 1.035210e-01 1.236214e-01 1.454566e-01 1.889879e-01
## theta[15] 2.328286e-01 2.520552e-01 2.725009e-01 3.136285e-01
## theta[16] 2.991278e-01 3.112420e-01 3.245367e-01 3.499842e-01
## theta[17] 2.020434e-01 2.246493e-01 2.493256e-01 2.937836e-01
## theta[18] 2.800892e-01 2.924864e-01 3.041737e-01 3.276909e-01
## theta[19] 2.206987e-01 2.436479e-01 2.669580e-01 3.196500e-01
## theta[20] 2.692327e-01 2.812761e-01 2.922780e-01 3.149402e-01
## theta[21] 2.410306e-01 2.537066e-01 2.668529e-01 2.907603e-01
## theta[22] 2.202353e-01 2.429761e-01 2.672002e-01 3.202652e-01
## theta[23] 2.757375e-01 2.866086e-01 2.972406e-01 3.195327e-01
## theta[24] 2.651719e-01 2.767454e-01 2.894013e-01 3.116428e-01
## theta[25] 2.288338e-01 2.418709e-01 2.551134e-01 2.820286e-01
## theta[26] 2.090025e-01 2.338495e-01 2.586017e-01 3.087830e-01
## theta[27] 2.764972e-01 2.885893e-01 2.994052e-01 3.239929e-01
## theta[28] 9.170092e-02 1.178254e-01 1.470238e-01 2.208658e-01
## theta[29] 2.189365e-01 2.382015e-01 2.582995e-01 2.947409e-01
## theta[30] 2.250938e-01 2.398515e-01 2.534590e-01 2.779180e-01
## theta[31] 2.863908e-01 2.961358e-01 3.079871e-01 3.315768e-01
## theta[32] 2.562387e-01 2.691525e-01 2.825925e-01 3.082527e-01
## theta[33] 1.179407e-01 1.427803e-01 1.723597e-01 2.312614e-01
## theta[34] 2.513953e-01 2.618485e-01 2.734766e-01 2.963533e-01
## theta[35] 2.276714e-01 2.429104e-01 2.583882e-01 2.903045e-01
## theta[36] 2.277740e-01 2.416189e-01 2.563840e-01 2.877926e-01
## theta[37] 1.105143e-01 1.383237e-01 1.701208e-01 2.443970e-01
## theta[38] 2.474801e-01 2.588513e-01 2.706415e-01 2.950260e-01
## theta[39] 9.247495e-02 1.195703e-01 1.493919e-01 2.210018e-01
## theta[40] 1.984004e-01 2.244102e-01 2.554015e-01 3.185489e-01
## theta[41] 2.829319e-01 2.953516e-01 3.098456e-01 3.344727e-01
## theta[42] 2.677132e-01 2.795241e-01 2.920293e-01 3.150985e-01
## theta[43] 2.534905e-01 2.719783e-01 2.907232e-01 3.300516e-01
## theta[44] 2.224504e-01 2.354084e-01 2.485180e-01 2.781440e-01
## theta[45] 1.002254e-01 1.280822e-01 1.556804e-01 2.286625e-01
## theta[46] 3.052744e-01 3.179475e-01 3.301709e-01 3.550764e-01
## theta[47] 2.418754e-01 2.729035e-01 3.056767e-01 3.709268e-01
## theta[48] 9.113008e-02 1.169149e-01 1.456323e-01 2.082595e-01
## theta[49] 1.996435e-01 2.137397e-01 2.283914e-01 2.552580e-01
## theta[50] 2.863551e-01 3.022478e-01 3.173116e-01 3.460308e-01
## theta[51] 2.040721e-01 2.226756e-01 2.421475e-01 2.816738e-01
## theta[52] 1.028079e-01 1.337159e-01 1.687630e-01 2.378053e-01
## theta[53] 1.130654e-01 1.457377e-01 1.842153e-01 2.633977e-01
## theta[54] 2.720728e-01 2.832089e-01 2.943539e-01 3.160073e-01
## theta[55] 9.205812e-02 1.146379e-01 1.380992e-01 1.964053e-01
## theta[56] 1.034840e-01 1.260975e-01 1.521587e-01 2.116690e-01
## theta[57] 2.168012e-01 2.355946e-01 2.526629e-01 2.868422e-01
## theta[58] 1.823521e-01 2.042214e-01 2.274169e-01 2.736588e-01
## theta[59] 2.642562e-01 2.773881e-01 2.917675e-01 3.207110e-01
## theta[60] 9.269835e-02 1.193952e-01 1.504991e-01 2.208579e-01
## theta[61] 2.825752e-01 2.940323e-01 3.058145e-01 3.292092e-01
## theta[62] 8.363251e-02 1.082089e-01 1.387069e-01 2.037968e-01
## theta[63] 2.565967e-01 2.669770e-01 2.788904e-01 3.012474e-01
## theta[64] 2.048823e-01 2.263612e-01 2.475292e-01 2.878174e-01
## theta[65] 2.819395e-01 2.936132e-01 3.053083e-01 3.298162e-01
## theta[66] 2.300788e-01 2.478120e-01 2.665503e-01 3.041128e-01
## theta[67] 2.537032e-01 2.776806e-01 3.036264e-01 3.538614e-01
## theta[68] 9.611608e-02 1.253250e-01 1.569193e-01 2.384074e-01
## theta[69] 8.028738e-02 9.890513e-02 1.203875e-01 1.706851e-01
## theta[70] 9.506065e-02 1.255456e-01 1.580128e-01 2.346018e-01
## theta[71] 2.279191e-01 2.453119e-01 2.625527e-01 3.015747e-01
## theta[72] 2.734322e-01 2.861626e-01 2.988887e-01 3.246135e-01
## theta[73] 7.589145e-02 9.821771e-02 1.248050e-01 1.863590e-01
## theta[74] 2.559585e-01 2.668794e-01 2.783460e-01 3.003107e-01
## theta[75] 2.939773e-01 3.052186e-01 3.174931e-01 3.378117e-01
## theta[76] 9.490736e-02 1.218731e-01 1.541730e-01 2.207130e-01
## theta[77] 1.987748e-01 2.235402e-01 2.493840e-01 3.020377e-01
## theta[78] 1.928380e-01 2.189623e-01 2.464567e-01 3.055958e-01
## theta[79] 2.015705e-01 2.294871e-01 2.564383e-01 3.116801e-01
## theta[80] 2.292721e-01 2.451116e-01 2.601968e-01 2.947157e-01
## theta[81] 2.050439e-01 2.204834e-01 2.375275e-01 2.738345e-01
## theta[82] 9.258875e-02 1.223173e-01 1.581149e-01 2.398154e-01
## theta[83] 9.559689e-02 1.229977e-01 1.577345e-01 2.328543e-01
## theta[84] 9.414298e-02 1.223397e-01 1.533974e-01 2.305092e-01
## theta[85] 1.123999e-01 1.387075e-01 1.697341e-01 2.445060e-01
## theta[86] 9.834416e-02 1.271935e-01 1.615516e-01 2.325009e-01
## theta[87] 1.056081e-01 1.322928e-01 1.661741e-01 2.440170e-01
## theta[88] 2.020067e-01 2.273151e-01 2.562997e-01 3.060188e-01
## theta[89] 2.102531e-01 2.289241e-01 2.498232e-01 2.904558e-01
## theta[90] 1.194756e-01 1.456291e-01 1.744773e-01 2.354391e-01
## theta[91] 2.565613e-01 2.694048e-01 2.827187e-01 3.080752e-01
## theta[92] 2.346236e-01 2.480985e-01 2.614315e-01 2.849861e-01
## theta[93] 1.058236e-01 1.368085e-01 1.732796e-01 2.598026e-01
## theta[94] 9.196705e-02 1.207080e-01 1.515246e-01 2.296195e-01
## theta[95] 2.111446e-01 2.373254e-01 2.645486e-01 3.240815e-01
## theta[96] 1.918722e-01 2.145126e-01 2.393450e-01 2.852726e-01
## theta[97] 2.140486e-01 2.265792e-01 2.390540e-01 2.668012e-01
## theta[98] 2.273095e-01 2.548057e-01 2.806823e-01 3.383317e-01
## theta[99] 2.628227e-01 2.786379e-01 2.951436e-01 3.304236e-01
## theta[100] 2.638953e-01 2.761538e-01 2.890623e-01 3.134044e-01
## theta[101] 2.391432e-01 2.623807e-01 2.843109e-01 3.322527e-01
## theta[102] 2.216907e-01 2.374567e-01 2.540290e-01 2.879199e-01
## theta[103] 1.909744e-01 2.029885e-01 2.159921e-01 2.394428e-01
## theta[104] 2.302293e-01 2.428913e-01 2.568661e-01 2.818910e-01
## theta[105] 1.969208e-01 2.134419e-01 2.300982e-01 2.632189e-01
## theta[106] 1.942666e-01 2.135980e-01 2.338288e-01 2.741689e-01
## theta[107] 2.215656e-01 2.523762e-01 2.849253e-01 3.538817e-01
## theta[108] 9.398614e-02 1.225675e-01 1.511603e-01 2.277349e-01
## theta[109] 2.384479e-01 2.612508e-01 2.901344e-01 3.453726e-01
## theta[110] 1.970438e-01 2.165701e-01 2.352682e-01 2.803497e-01
## theta[111] 1.912774e-01 2.111801e-01 2.324138e-01 2.681559e-01
## theta[112] 2.583140e-01 2.696952e-01 2.832782e-01 3.047274e-01
## theta[113] 2.080834e-01 2.284553e-01 2.498219e-01 2.938975e-01
## theta[114] 2.383924e-01 2.547760e-01 2.716494e-01 3.053854e-01
## theta[115] 2.049083e-01 2.260590e-01 2.482832e-01 2.895749e-01
## theta[116] 2.027849e-01 2.165742e-01 2.287839e-01 2.545813e-01
## theta[117] 2.244576e-01 2.371100e-01 2.508619e-01 2.770465e-01
## theta[118] 9.364598e-02 1.234078e-01 1.558825e-01 2.339051e-01
## theta[119] 1.032482e-01 1.309387e-01 1.629161e-01 2.332420e-01
## theta[120] 2.187248e-01 2.313157e-01 2.434997e-01 2.683054e-01
## theta[121] 1.995429e-01 2.211899e-01 2.432230e-01 2.851457e-01
## theta[122] 8.988982e-02 1.198142e-01 1.546826e-01 2.243121e-01
## theta[123] 2.107170e-01 2.313415e-01 2.516291e-01 2.952736e-01
## theta[124] 2.429986e-01 2.641771e-01 2.912011e-01 3.352114e-01
## theta[125] 1.129637e-01 1.336095e-01 1.547413e-01 2.039959e-01
## theta[126] 1.743355e-01 1.924904e-01 2.104767e-01 2.497446e-01
## theta[127] 1.081593e-01 1.347344e-01 1.674800e-01 2.406161e-01
## theta[128] 1.037485e-01 1.332086e-01 1.642838e-01 2.404017e-01
## theta[129] 2.076541e-01 2.354309e-01 2.651553e-01 3.317760e-01
## theta[130] 2.096161e-01 2.366603e-01 2.657783e-01 3.295392e-01
## theta[131] 2.418322e-01 2.556609e-01 2.709404e-01 2.994106e-01
## theta[132] 1.978392e-01 2.116030e-01 2.249403e-01 2.532055e-01
## theta[133] 2.563059e-01 2.684512e-01 2.798811e-01 3.041394e-01
## theta[134] 9.358319e-02 1.131409e-01 1.370220e-01 1.845070e-01
## theta[135] 8.982757e-02 1.214621e-01 1.560350e-01 2.286783e-01
## theta[136] 3.079647e-01 3.208480e-01 3.336337e-01 3.574472e-01
## theta[137] 2.326398e-01 2.448758e-01 2.568659e-01 2.799635e-01
## theta[138] 2.463836e-01 2.676086e-01 2.865103e-01 3.276675e-01
## theta[139] 9.258857e-02 1.239330e-01 1.585461e-01 2.389697e-01
## theta[140] 2.550641e-01 2.672879e-01 2.788216e-01 3.012529e-01
## theta[141] 2.324561e-01 2.547864e-01 2.776555e-01 3.213687e-01
## theta[142] 2.456194e-01 2.595291e-01 2.728377e-01 3.002986e-01
## theta[143] 2.813803e-01 2.937008e-01 3.067924e-01 3.304550e-01
## theta[144] 2.521239e-01 2.636398e-01 2.756236e-01 2.976003e-01
## theta[145] 2.125540e-01 2.346917e-01 2.572801e-01 3.049089e-01
## theta[146] 1.956346e-01 2.062874e-01 2.173732e-01 2.395081e-01
## theta[147] 2.435740e-01 2.580566e-01 2.742235e-01 3.046319e-01
## theta[148] 2.927989e-01 3.072244e-01 3.218492e-01 3.555916e-01
## theta[149] 2.378714e-01 2.490670e-01 2.612375e-01 2.870759e-01
## theta[150] 1.100607e-01 1.378972e-01 1.712748e-01 2.426032e-01
## theta[151] 2.159786e-01 2.437820e-01 2.717474e-01 3.267997e-01
## theta[152] 1.110545e-01 1.399594e-01 1.785880e-01 2.510487e-01
## theta[153] 1.245931e-01 1.516491e-01 1.781737e-01 2.342267e-01
## theta[154] 1.064687e-01 1.357045e-01 1.682480e-01 2.402496e-01
## theta[155] 1.078380e-01 1.379533e-01 1.716114e-01 2.430415e-01
## theta[156] 2.204172e-01 2.321660e-01 2.459572e-01 2.680748e-01
## theta[157] 2.118706e-01 2.256227e-01 2.400457e-01 2.646339e-01
## theta[158] 2.186561e-01 2.330152e-01 2.480030e-01 2.746678e-01
## theta[159] 9.389692e-02 1.208233e-01 1.523101e-01 2.225107e-01
## theta[160] 2.246110e-01 2.428737e-01 2.627151e-01 2.977362e-01
## theta[161] 9.202359e-02 1.211947e-01 1.529947e-01 2.291673e-01
## theta[162] 1.315752e-01 1.572422e-01 1.839056e-01 2.391721e-01
## theta[163] 8.074900e-02 1.054964e-01 1.375356e-01 2.067937e-01
## theta[164] 2.383301e-01 2.599104e-01 2.805281e-01 3.203270e-01
## theta[165] 2.499693e-01 2.684536e-01 2.903727e-01 3.339944e-01
## theta[166] 2.012508e-01 2.286554e-01 2.541572e-01 3.057559e-01
## theta[167] 2.695660e-01 2.821564e-01 2.938828e-01 3.161249e-01
## theta[168] 2.398370e-01 2.539093e-01 2.677414e-01 2.977207e-01
## theta[169] 2.667802e-01 2.795922e-01 2.940683e-01 3.196279e-01
## theta[170] 1.893809e-01 2.066353e-01 2.239614e-01 2.597514e-01
## theta[171] 8.737012e-02 1.165237e-01 1.456643e-01 2.199133e-01
## theta[172] 8.966903e-02 1.093775e-01 1.324951e-01 1.815959e-01
## theta[173] 1.757978e-01 1.950085e-01 2.152873e-01 2.557356e-01
## theta[174] 2.553889e-01 2.674813e-01 2.793988e-01 2.997568e-01
## theta[175] 2.705825e-01 2.843100e-01 2.994830e-01 3.304529e-01
## theta[176] 2.260872e-01 2.528240e-01 2.814001e-01 3.350568e-01
## theta[177] 2.472716e-01 2.653006e-01 2.823256e-01 3.152833e-01
## theta[178] 2.308458e-01 2.516006e-01 2.721529e-01 3.162326e-01
## theta[179] 2.469779e-01 2.601395e-01 2.744343e-01 2.979645e-01
## theta[180] 1.799212e-01 2.059413e-01 2.314258e-01 2.862412e-01
## theta[181] 2.230372e-01 2.387379e-01 2.555572e-01 2.886187e-01
## theta[182] 2.630518e-01 2.759945e-01 2.893480e-01 3.130739e-01
## theta[183] 9.490135e-02 1.214610e-01 1.542079e-01 2.255166e-01
## theta[184] 8.742691e-02 1.150170e-01 1.509470e-01 2.254987e-01
## theta[185] 2.768264e-01 2.909736e-01 3.061260e-01 3.313743e-01
## theta[186] 2.223228e-01 2.381297e-01 2.539203e-01 2.859665e-01
## theta[187] 9.191566e-02 1.182673e-01 1.487395e-01 2.213910e-01
## theta[188] 1.015084e-01 1.302236e-01 1.599111e-01 2.321590e-01
## theta[189] 8.484182e-02 1.148771e-01 1.468597e-01 2.297147e-01
## theta[190] 1.044029e-01 1.367567e-01 1.712464e-01 2.424321e-01
## theta[191] 1.787673e-01 1.933678e-01 2.087790e-01 2.408878e-01
## theta[192] 2.172442e-01 2.375794e-01 2.584941e-01 2.951056e-01
## theta[193] 1.182835e-01 1.441216e-01 1.718543e-01 2.363620e-01
## theta[194] 8.781554e-02 1.094244e-01 1.329398e-01 1.927849e-01
## theta[195] 8.960032e-02 1.191097e-01 1.485190e-01 2.288289e-01
## theta[196] 9.200721e-02 1.224544e-01 1.597573e-01 2.376914e-01
## theta[197] 1.460298e-01 1.697900e-01 1.943089e-01 2.488329e-01
## theta[198] 9.314872e-02 1.174621e-01 1.501621e-01 2.248448e-01
## theta[199] 8.472512e-02 1.026849e-01 1.222483e-01 1.624808e-01
## theta[200] 2.072377e-01 2.329625e-01 2.596787e-01 3.112205e-01
## theta[201] 2.089530e-01 2.204596e-01 2.318024e-01 2.554632e-01
## theta[202] 2.191340e-01 2.312740e-01 2.438126e-01 2.699811e-01
## theta[203] 2.463844e-01 2.590969e-01 2.717377e-01 3.006154e-01
## theta[204] 2.117104e-01 2.266499e-01 2.416447e-01 2.681320e-01
## theta[205] 2.526188e-01 2.647440e-01 2.773777e-01 3.020206e-01
## theta[206] 1.230040e-01 1.534070e-01 1.879926e-01 2.817804e-01
## theta[207] 2.172374e-01 2.277922e-01 2.380175e-01 2.570795e-01
## theta[208] 1.543758e-01 1.748486e-01 2.018086e-01 2.578096e-01
## theta[209] 2.375177e-01 2.586477e-01 2.794874e-01 3.168048e-01
## theta[210] 8.766879e-02 1.141198e-01 1.465669e-01 2.129770e-01
## theta[211] 2.074477e-01 2.328876e-01 2.618227e-01 3.113016e-01
## theta[212] 2.163208e-01 2.393443e-01 2.646329e-01 3.126742e-01
## theta[213] 2.122061e-01 2.374396e-01 2.632857e-01 3.073325e-01
## theta[214] 2.564274e-01 2.679010e-01 2.797047e-01 2.997365e-01
## theta[215] 9.571542e-02 1.225538e-01 1.511773e-01 2.275657e-01
## theta[216] 7.943775e-02 1.033964e-01 1.290804e-01 1.888858e-01
## theta[217] 8.953057e-02 1.168807e-01 1.507136e-01 2.180996e-01
## theta[218] 2.742863e-01 2.911291e-01 3.078180e-01 3.416640e-01
## theta[219] 8.566012e-02 1.131108e-01 1.460866e-01 2.161960e-01
## theta[220] 8.628101e-02 1.155575e-01 1.489739e-01 2.186632e-01
## theta[221] 2.240927e-01 2.348301e-01 2.454790e-01 2.676656e-01
## theta[222] 9.230541e-02 1.190988e-01 1.523198e-01 2.358902e-01
## theta[223] 9.398914e-02 1.176592e-01 1.460449e-01 2.057672e-01
## theta[224] 8.880564e-02 1.147663e-01 1.483655e-01 2.175842e-01
## theta[225] 9.482168e-02 1.252624e-01 1.599811e-01 2.323928e-01
## theta[226] 2.435439e-01 2.688133e-01 2.964947e-01 3.540696e-01
## theta[227] 9.236774e-02 1.224654e-01 1.546083e-01 2.332373e-01
## theta[228] 2.141384e-01 2.253565e-01 2.357494e-01 2.565439e-01
## theta[229] 9.115683e-02 1.181024e-01 1.480852e-01 2.215195e-01
## theta[230] 2.197018e-01 2.325674e-01 2.456654e-01 2.703149e-01
## theta[231] 1.065022e-01 1.319482e-01 1.636420e-01 2.281170e-01
## theta[232] 2.715876e-01 2.842685e-01 2.956114e-01 3.201220e-01
## theta[233] 2.296016e-01 2.438469e-01 2.586421e-01 2.910898e-01
## theta[234] 2.373852e-01 2.481387e-01 2.585588e-01 2.815235e-01
## theta[235] 1.957468e-01 2.130340e-01 2.311581e-01 2.665008e-01
## theta[236] 2.148996e-01 2.342413e-01 2.545623e-01 2.982608e-01
## theta[237] 2.088896e-01 2.269130e-01 2.459971e-01 2.830041e-01
## theta[238] 2.361989e-01 2.535634e-01 2.733488e-01 3.059276e-01
## theta[239] 2.485064e-01 2.732523e-01 2.978677e-01 3.547860e-01
## theta[240] 2.088452e-01 2.281311e-01 2.484086e-01 2.867919e-01
## theta[241] 2.403755e-01 2.524206e-01 2.655332e-01 2.895885e-01
## theta[242] 2.429309e-01 2.644397e-01 2.871309e-01 3.326963e-01
## theta[243] 2.613293e-01 2.780337e-01 2.982742e-01 3.354542e-01
## theta[244] 2.500895e-01 2.617003e-01 2.742729e-01 2.960154e-01
## theta[245] 2.755056e-01 2.876303e-01 3.000124e-01 3.254652e-01
## theta[246] 1.140044e-01 1.463184e-01 1.821493e-01 2.653328e-01
## theta[247] 9.490251e-02 1.211987e-01 1.528169e-01 2.335805e-01
## theta[248] 2.239978e-01 2.466364e-01 2.713631e-01 3.208663e-01
## theta[249] 2.793729e-01 2.924469e-01 3.050420e-01 3.311657e-01
## theta[250] 2.856269e-01 3.026185e-01 3.180480e-01 3.509184e-01
## theta[251] 8.653272e-02 1.159417e-01 1.456602e-01 2.203978e-01
## theta[252] 2.312665e-01 2.489710e-01 2.672970e-01 2.994145e-01
## theta[253] 2.869449e-01 2.981805e-01 3.098824e-01 3.296341e-01
## theta[254] 2.435433e-01 2.554693e-01 2.673350e-01 2.897694e-01
## theta[255] 2.163941e-01 2.309078e-01 2.453891e-01 2.749439e-01
## theta[256] 2.517424e-01 2.634078e-01 2.759615e-01 2.979050e-01
## theta[257] 2.665965e-01 2.794018e-01 2.916167e-01 3.160309e-01
## theta[258] 2.334297e-01 2.635899e-01 2.928024e-01 3.689839e-01
## theta[259] 9.283400e-02 1.217537e-01 1.533094e-01 2.331841e-01
## theta[260] 2.964243e-01 3.082963e-01 3.196419e-01 3.433172e-01
## theta[261] 1.224077e-01 1.531599e-01 1.883090e-01 2.780968e-01
## theta[262] 1.942180e-01 2.116875e-01 2.294760e-01 2.643971e-01
## theta[263] 2.337693e-01 2.451301e-01 2.567829e-01 2.789827e-01
## theta[264] 2.021694e-01 2.207502e-01 2.395473e-01 2.766500e-01
## theta[265] 2.395664e-01 2.552357e-01 2.710355e-01 3.035116e-01
## theta[266] 2.789041e-01 2.921518e-01 3.060211e-01 3.301351e-01
## theta[267] 2.301299e-01 2.565329e-01 2.860900e-01 3.425875e-01
## theta[268] 1.088744e-01 1.329818e-01 1.605872e-01 2.182575e-01
## theta[269] 2.353924e-01 2.624364e-01 2.873759e-01 3.378022e-01
## theta[270] 2.660644e-01 2.823386e-01 2.993943e-01 3.334745e-01
## theta[271] 2.255905e-01 2.427245e-01 2.598795e-01 2.935002e-01
## theta[272] 2.018758e-01 2.193422e-01 2.398249e-01 2.761718e-01
## theta[273] 2.131002e-01 2.329646e-01 2.532508e-01 2.880606e-01
## theta[274] 2.673669e-01 2.827405e-01 2.992269e-01 3.310860e-01
## theta[275] 9.110986e-02 1.176871e-01 1.487901e-01 2.244344e-01
## theta[276] 1.947985e-01 2.143608e-01 2.350206e-01 2.772986e-01
## theta[277] 9.211864e-02 1.218373e-01 1.525739e-01 2.183371e-01
## theta[278] 1.326635e-01 1.592361e-01 1.922011e-01 2.612765e-01
## theta[279] 8.980094e-02 1.198960e-01 1.539767e-01 2.363060e-01
## theta[280] 2.084009e-01 2.196745e-01 2.313836e-01 2.539856e-01
## theta[281] 2.316667e-01 2.494031e-01 2.678471e-01 3.076416e-01
## theta[282] 9.336855e-02 1.203428e-01 1.517741e-01 2.279343e-01
## theta[283] 2.186670e-01 2.288056e-01 2.395541e-01 2.611708e-01
## theta[284] 9.254811e-02 1.220459e-01 1.544615e-01 2.331577e-01
## theta[285] 2.709871e-01 2.830497e-01 2.951447e-01 3.168231e-01
## theta[286] 7.976419e-02 9.784648e-02 1.187936e-01 1.637815e-01
## theta[287] 2.112931e-01 2.305634e-01 2.499526e-01 2.908543e-01
## theta[288] 2.443267e-01 2.676765e-01 2.942746e-01 3.413446e-01
## theta[289] 9.289390e-02 1.223495e-01 1.533920e-01 2.244535e-01
## theta[290] 2.643184e-01 2.763720e-01 2.884600e-01 3.119926e-01
## theta[291] 1.555314e-01 1.785426e-01 2.051034e-01 2.640578e-01
## theta[292] 2.227955e-01 2.461072e-01 2.687888e-01 3.198266e-01
## theta[293] 1.932773e-01 2.200837e-01 2.488235e-01 3.038725e-01
## theta[294] 2.352096e-01 2.504842e-01 2.673517e-01 3.019812e-01
## theta[295] 2.285459e-01 2.433495e-01 2.584237e-01 2.889372e-01
## theta[296] 8.953480e-02 1.204165e-01 1.549058e-01 2.303857e-01
## theta[297] 2.705431e-01 2.814224e-01 2.920444e-01 3.156571e-01
## theta[298] 2.419817e-01 2.587944e-01 2.753782e-01 3.063329e-01
## theta[299] 2.102821e-01 2.270464e-01 2.447503e-01 2.823099e-01
## theta[300] 2.010700e-01 2.173731e-01 2.374324e-01 2.732509e-01
## theta[301] 2.596586e-01 2.735827e-01 2.899295e-01 3.177707e-01
## theta[302] 2.090190e-01 2.375851e-01 2.665418e-01 3.245759e-01
## theta[303] 2.206702e-01 2.487823e-01 2.769964e-01 3.362708e-01
## theta[304] 9.208412e-02 1.203151e-01 1.550828e-01 2.244700e-01
## theta[305] 2.035347e-01 2.208600e-01 2.406078e-01 2.723381e-01
## theta[306] 2.243667e-01 2.351525e-01 2.460763e-01 2.690557e-01
## theta[307] 1.849656e-01 2.042840e-01 2.248601e-01 2.657452e-01
## theta[308] 1.406630e-01 1.691554e-01 2.009920e-01 2.637408e-01
## theta[309] 2.230781e-01 2.376349e-01 2.521349e-01 2.789511e-01
## theta[310] 2.705509e-01 2.835839e-01 2.969264e-01 3.204177e-01
## theta[311] 9.488933e-02 1.171694e-01 1.413006e-01 1.962288e-01
## theta[312] 2.181835e-01 2.402282e-01 2.629751e-01 3.119815e-01
## theta[313] 2.263911e-01 2.447112e-01 2.632859e-01 3.033647e-01
## theta[314] 8.708744e-02 1.130939e-01 1.420620e-01 2.065856e-01
## theta[315] 1.058884e-01 1.361606e-01 1.682212e-01 2.363488e-01
## theta[316] 2.208676e-01 2.529366e-01 2.823580e-01 3.493073e-01
## theta[317] 2.641215e-01 2.810659e-01 2.963708e-01 3.249587e-01
## theta[318] 2.326606e-01 2.463240e-01 2.616281e-01 2.870237e-01
## theta[319] 2.413473e-01 2.596790e-01 2.775023e-01 3.159943e-01
## theta[320] 9.775163e-02 1.257566e-01 1.572822e-01 2.379939e-01
## theta[321] 1.084959e-01 1.405553e-01 1.713354e-01 2.413718e-01
## theta[322] 1.011128e-01 1.295342e-01 1.627383e-01 2.292563e-01
## theta[323] 2.243326e-01 2.419508e-01 2.611738e-01 3.005304e-01
## theta[324] 9.037679e-02 1.204539e-01 1.510710e-01 2.201109e-01
## theta[325] 9.294805e-02 1.231802e-01 1.567719e-01 2.352924e-01
## theta[326] 2.019699e-01 2.331331e-01 2.639347e-01 3.317052e-01
## theta[327] 9.108908e-02 1.185741e-01 1.505782e-01 2.254276e-01
## theta[328] 2.089738e-01 2.355209e-01 2.637851e-01 3.167857e-01
## theta[329] 2.381138e-01 2.588213e-01 2.773176e-01 3.199061e-01
## theta[330] 1.061283e-01 1.364889e-01 1.764905e-01 2.577153e-01
## theta[331] 2.456045e-01 2.576230e-01 2.692464e-01 2.912048e-01
## theta[332] 2.180787e-01 2.335000e-01 2.505622e-01 2.866097e-01
## theta[333] 2.143164e-01 2.258965e-01 2.394356e-01 2.666276e-01
## theta[334] 2.571142e-01 2.692318e-01 2.822525e-01 3.049755e-01
## theta[335] 8.839206e-02 1.196025e-01 1.548903e-01 2.249826e-01
## theta[336] 9.328464e-02 1.230613e-01 1.610758e-01 2.300731e-01
## theta[337] 2.020258e-01 2.293158e-01 2.555677e-01 3.103795e-01
## theta[338] 9.212192e-02 1.220592e-01 1.536299e-01 2.335876e-01
## theta[339] 2.026259e-01 2.196285e-01 2.364921e-01 2.693964e-01
## theta[340] 1.937756e-01 2.068258e-01 2.202120e-01 2.456586e-01
## theta[341] 2.495082e-01 2.670996e-01 2.843387e-01 3.229268e-01
## theta[342] 2.568838e-01 2.703888e-01 2.837964e-01 3.104153e-01
## theta[343] 2.698471e-01 2.841219e-01 2.980574e-01 3.217829e-01
## theta[344] 2.183091e-01 2.429599e-01 2.662845e-01 3.113871e-01
## theta[345] 8.989830e-02 1.086544e-01 1.285674e-01 1.746514e-01
## theta[346] 2.255611e-01 2.355875e-01 2.478421e-01 2.712436e-01
## theta[347] 1.977597e-01 2.156382e-01 2.349326e-01 2.726342e-01
## theta[348] 9.194681e-02 1.209624e-01 1.504654e-01 2.280113e-01
## theta[349] 2.626973e-01 2.780848e-01 2.925644e-01 3.198902e-01
## theta[350] 2.327037e-01 2.454564e-01 2.589002e-01 2.844742e-01
## theta[351] 1.069504e-01 1.347501e-01 1.672632e-01 2.468851e-01
## theta[352] 2.023016e-01 2.299000e-01 2.619103e-01 3.300358e-01
## theta[353] 1.971085e-01 2.241541e-01 2.498565e-01 3.065637e-01
## theta[354] 2.462751e-01 2.570797e-01 2.673051e-01 2.903980e-01
## theta[355] 2.332842e-01 2.639794e-01 2.943451e-01 3.571797e-01
## theta[356] 2.161226e-01 2.393177e-01 2.629325e-01 3.081495e-01
## theta[357] 1.198965e-01 1.482889e-01 1.841907e-01 2.707758e-01
## theta[358] 2.512152e-01 2.682089e-01 2.852799e-01 3.206146e-01
## theta[359] 9.415186e-02 1.223828e-01 1.550829e-01 2.349144e-01
## theta[360] 1.960035e-01 2.174545e-01 2.388810e-01 2.811425e-01
## theta[361] 2.263050e-01 2.552092e-01 2.854141e-01 3.555649e-01
## theta[362] 1.796500e-01 1.984264e-01 2.188595e-01 2.589278e-01
## theta[363] 8.944543e-02 1.172561e-01 1.503154e-01 2.330682e-01
## theta[364] 9.810236e-02 1.178492e-01 1.380826e-01 1.854177e-01
## theta[365] 2.695619e-01 2.817437e-01 2.946600e-01 3.189022e-01
## theta[366] 2.155443e-01 2.343659e-01 2.533609e-01 2.907403e-01
## theta[367] 2.422303e-01 2.537493e-01 2.649272e-01 2.851643e-01
## theta[368] 2.721132e-01 2.853194e-01 2.990406e-01 3.278061e-01
## theta[369] 8.176839e-02 1.003638e-01 1.241159e-01 1.675456e-01
## theta[370] 2.452380e-01 2.554063e-01 2.657099e-01 2.865662e-01
## theta[371] 2.021350e-01 2.199416e-01 2.370480e-01 2.736355e-01
## theta[372] 2.680271e-01 2.789395e-01 2.891157e-01 3.097228e-01
## theta[373] 2.682597e-01 2.894603e-01 3.114731e-01 3.585834e-01
## theta[374] 2.171326e-01 2.405586e-01 2.637722e-01 3.127417e-01
## theta[375] 9.985480e-02 1.301140e-01 1.636909e-01 2.304694e-01
## theta[376] 2.317169e-01 2.459852e-01 2.611691e-01 2.901380e-01
## theta[377] 7.273953e-02 9.780799e-02 1.234980e-01 1.823140e-01
## theta[378] 2.529252e-01 2.665829e-01 2.815952e-01 3.122341e-01
## theta[379] 1.540808e-01 1.803191e-01 2.094894e-01 2.726340e-01
## theta[380] 8.924720e-02 1.135376e-01 1.426744e-01 2.077891e-01
## theta[381] 9.013462e-02 1.197756e-01 1.511329e-01 2.272829e-01
## theta[382] 1.958850e-01 2.190236e-01 2.431243e-01 2.934626e-01
## theta[383] 8.456355e-02 1.115282e-01 1.446298e-01 2.116741e-01
## theta[384] 1.030821e-01 1.246647e-01 1.466679e-01 1.949243e-01
## theta[385] 2.157991e-01 2.446852e-01 2.719560e-01 3.255422e-01
## theta[386] 2.364999e-01 2.499651e-01 2.633152e-01 2.884157e-01
## theta[387] 1.133331e-01 1.336766e-01 1.558914e-01 2.089118e-01
## theta[388] 8.983967e-02 1.189161e-01 1.565767e-01 2.343165e-01
## theta[389] 1.042936e-01 1.296488e-01 1.627042e-01 2.345243e-01
## theta[390] 2.506579e-01 2.643301e-01 2.772212e-01 3.033658e-01
## theta[391] 9.609613e-02 1.234450e-01 1.533287e-01 2.333643e-01
## theta[392] 1.014706e-01 1.280551e-01 1.575755e-01 2.241868e-01
## theta[393] 9.357343e-02 1.218190e-01 1.555808e-01 2.432654e-01
## theta[394] 2.421778e-01 2.581077e-01 2.739254e-01 3.040889e-01
## theta[395] 8.517956e-02 1.106331e-01 1.402009e-01 2.041538e-01
## theta[396] 2.136290e-01 2.253595e-01 2.375713e-01 2.658003e-01
## theta[397] 1.697931e-01 1.897026e-01 2.113859e-01 2.508772e-01
## theta[398] 1.791014e-01 1.945133e-01 2.093158e-01 2.422927e-01
## theta[399] 8.659273e-02 1.148036e-01 1.442481e-01 2.159293e-01
## theta[400] 2.344653e-01 2.582236e-01 2.823333e-01 3.315357e-01
## theta[401] 2.365145e-01 2.516692e-01 2.677881e-01 2.995338e-01
## theta[402] 2.051058e-01 2.226654e-01 2.415784e-01 2.811824e-01
## theta[403] 2.219873e-01 2.414226e-01 2.599572e-01 3.002868e-01
## theta[404] 8.525143e-02 1.161723e-01 1.485390e-01 2.190965e-01
## theta[405] 2.568993e-01 2.684144e-01 2.801042e-01 3.013827e-01
## theta[406] 2.430853e-01 2.552610e-01 2.674684e-01 2.888272e-01
## theta[407] 2.409455e-01 2.532267e-01 2.648196e-01 2.862061e-01
## theta[408] 1.588330e-01 1.888237e-01 2.195806e-01 2.835722e-01
## theta[409] 2.291231e-01 2.583523e-01 2.915507e-01 3.570037e-01
## theta[410] 2.112110e-01 2.393321e-01 2.676921e-01 3.261384e-01
## theta[411] 1.207772e-01 1.513892e-01 1.851721e-01 2.619340e-01
## theta[412] 2.407982e-01 2.528299e-01 2.652515e-01 2.886341e-01
## theta[413] 2.303381e-01 2.464839e-01 2.639404e-01 3.009910e-01
## theta[414] 2.728908e-01 2.892036e-01 3.042453e-01 3.364381e-01
## theta[415] 2.365480e-01 2.543077e-01 2.749042e-01 3.123642e-01
## theta[416] 1.018440e-01 1.316307e-01 1.681203e-01 2.469068e-01
## theta[417] 2.309480e-01 2.444560e-01 2.577073e-01 2.879001e-01
## theta[418] 2.283877e-01 2.457237e-01 2.635707e-01 2.984522e-01
## theta[419] 1.979534e-01 2.210475e-01 2.440844e-01 2.929758e-01
## theta[420] 2.082530e-01 2.317235e-01 2.586355e-01 3.131147e-01
## theta[421] 7.915240e-02 1.007031e-01 1.249022e-01 1.783043e-01
## theta[422] 2.272879e-01 2.382746e-01 2.496596e-01 2.696236e-01
## theta[423] 9.334220e-02 1.161360e-01 1.425179e-01 2.051913e-01
## theta[424] 2.964640e-01 3.102761e-01 3.248629e-01 3.537371e-01
## theta[425] 9.050191e-02 1.152366e-01 1.473204e-01 2.090943e-01
## theta[426] 2.061078e-01 2.224804e-01 2.393405e-01 2.720980e-01
## theta[427] 9.185875e-02 1.114930e-01 1.345744e-01 1.788611e-01
## theta[428] 9.319567e-02 1.206747e-01 1.555596e-01 2.186387e-01
## theta[429] 2.132428e-01 2.250598e-01 2.367815e-01 2.622140e-01
## theta[430] 8.938600e-02 1.194418e-01 1.517839e-01 2.241845e-01
## theta[431] 1.051454e-01 1.368635e-01 1.753145e-01 2.533855e-01
## theta[432] 9.582087e-02 1.216983e-01 1.561888e-01 2.235694e-01
## theta[433] 8.615385e-02 1.079072e-01 1.351643e-01 1.975365e-01
## theta[434] 9.012361e-02 1.161109e-01 1.444642e-01 2.065062e-01
## theta[435] 9.237798e-02 1.209280e-01 1.514584e-01 2.290407e-01
## theta[436] 2.298640e-01 2.551372e-01 2.817860e-01 3.383650e-01
## theta[437] 1.083815e-01 1.381408e-01 1.726127e-01 2.476744e-01
## theta[438] 2.093395e-01 2.328147e-01 2.579360e-01 3.112745e-01
## theta[439] 9.019559e-02 1.171524e-01 1.481365e-01 2.195326e-01
## theta[440] 2.053509e-01 2.191371e-01 2.328139e-01 2.628369e-01
## theta[441] 2.332733e-01 2.474234e-01 2.614354e-01 2.911210e-01
## theta[442] 2.446807e-01 2.561920e-01 2.681354e-01 2.912484e-01
## theta[443] 9.524536e-02 1.226075e-01 1.557725e-01 2.391665e-01
## theta[444] 2.345312e-01 2.569295e-01 2.841244e-01 3.386353e-01
## theta[445] 2.289306e-01 2.405316e-01 2.520191e-01 2.746595e-01
## theta[446] 1.511315e-01 1.791338e-01 2.110359e-01 2.732887e-01
## theta[447] 2.342463e-01 2.523718e-01 2.733303e-01 3.073431e-01
## theta[448] 2.073363e-01 2.277069e-01 2.482776e-01 2.922302e-01
## theta[449] 2.389382e-01 2.500026e-01 2.611284e-01 2.816930e-01
## theta[450] 2.507193e-01 2.645568e-01 2.788414e-01 3.075633e-01
## theta[451] 7.937681e-02 9.909503e-02 1.184356e-01 1.604018e-01
## theta[452] 2.174248e-01 2.435722e-01 2.718545e-01 3.283836e-01
## theta[453] 2.064923e-01 2.219085e-01 2.388328e-01 2.694543e-01
## theta[454] 2.965485e-01 3.073291e-01 3.186590e-01 3.441193e-01
## theta[455] 8.796340e-02 1.093771e-01 1.337378e-01 1.911977e-01
## theta[456] 9.360347e-02 1.203801e-01 1.565999e-01 2.237562e-01
## theta[457] 1.112080e-01 1.404945e-01 1.749641e-01 2.575209e-01
## theta[458] 9.786497e-02 1.280223e-01 1.600682e-01 2.327489e-01
## theta[459] 3.027009e-01 3.180994e-01 3.330661e-01 3.610958e-01
## theta[460] 8.801342e-02 1.074747e-01 1.326666e-01 1.854131e-01
## theta[461] 9.239808e-02 1.219498e-01 1.543085e-01 2.242761e-01
## theta[462] 2.218091e-01 2.369031e-01 2.543835e-01 2.906873e-01
## theta[463] 1.900885e-01 2.021986e-01 2.157872e-01 2.416326e-01
## theta[464] 9.006697e-02 1.178809e-01 1.494478e-01 2.339955e-01
## theta[465] 2.053576e-01 2.257121e-01 2.466782e-01 2.945673e-01
## theta[466] 2.496807e-01 2.649755e-01 2.823247e-01 3.124673e-01
## theta[467] 9.580252e-02 1.230505e-01 1.526790e-01 2.264736e-01
## theta[468] 8.754910e-02 1.061384e-01 1.265478e-01 1.654508e-01
## theta[469] 2.146685e-01 2.301128e-01 2.461023e-01 2.744140e-01
## theta[470] 2.242760e-01 2.416283e-01 2.589037e-01 2.916375e-01
## theta[471] 2.820778e-01 2.967057e-01 3.104255e-01 3.357836e-01
## theta[472] 8.866921e-02 1.151854e-01 1.451269e-01 2.154481e-01
## theta[473] 2.420766e-01 2.575004e-01 2.750322e-01 3.082449e-01
## theta[474] 2.863707e-01 3.012892e-01 3.161169e-01 3.455440e-01
## theta[475] 8.815022e-02 1.151330e-01 1.441291e-01 2.116994e-01
## theta[476] 1.480220e-01 1.736052e-01 2.009854e-01 2.520906e-01
## theta[477] 2.450578e-01 2.587031e-01 2.730698e-01 3.044775e-01
## theta[478] 2.148254e-01 2.357274e-01 2.577457e-01 3.044642e-01
## theta[479] 1.158442e-01 1.381006e-01 1.648980e-01 2.133644e-01
## theta[480] 2.876402e-01 2.999678e-01 3.117608e-01 3.378632e-01
## theta[481] 2.081273e-01 2.211503e-01 2.351556e-01 2.637969e-01
## theta[482] 1.382382e-01 1.607332e-01 1.834072e-01 2.359684e-01
## theta[483] 2.253238e-01 2.422399e-01 2.591353e-01 2.964878e-01
## theta[484] 2.066561e-01 2.309526e-01 2.550024e-01 3.019713e-01
## theta[485] 1.202949e-01 1.506749e-01 1.865726e-01 2.668175e-01
## theta[486] 2.706752e-01 2.834406e-01 2.952105e-01 3.150824e-01
## theta[487] 2.260314e-01 2.466024e-01 2.693264e-01 3.176106e-01
## theta[488] 1.678023e-01 1.897607e-01 2.105763e-01 2.531965e-01
## theta[489] 2.102354e-01 2.272007e-01 2.436763e-01 2.822417e-01
## theta[490] 2.321184e-01 2.485373e-01 2.651914e-01 2.998116e-01
## theta[491] 9.896191e-02 1.273300e-01 1.641233e-01 2.421965e-01
## theta[492] 2.132018e-01 2.282083e-01 2.438274e-01 2.756445e-01
## theta[493] 9.130994e-02 1.194756e-01 1.503522e-01 2.308940e-01
## theta[494] 2.341086e-01 2.470111e-01 2.614479e-01 2.868337e-01
## theta[495] 8.055538e-02 1.028662e-01 1.301334e-01 1.870868e-01
## theta[496] 8.570996e-02 1.102593e-01 1.374415e-01 2.043753e-01
## theta[497] 2.296528e-01 2.449916e-01 2.596200e-01 2.896352e-01
## theta[498] 2.686421e-01 2.814922e-01 2.945514e-01 3.170163e-01
## theta[499] 2.215254e-01 2.379187e-01 2.547349e-01 2.841392e-01
## theta[500] 9.131191e-02 1.105933e-01 1.307137e-01 1.715689e-01
## theta[501] 9.092325e-02 1.169440e-01 1.454547e-01 2.151996e-01
## theta[502] 2.324632e-01 2.436467e-01 2.556614e-01 2.772650e-01
## theta[503] 9.116574e-02 1.168632e-01 1.454095e-01 2.088060e-01
## theta[504] 2.517238e-01 2.676058e-01 2.832574e-01 3.147481e-01
## theta[505] 9.300220e-02 1.230604e-01 1.560719e-01 2.306846e-01
## theta[506] 2.205956e-01 2.338963e-01 2.473578e-01 2.738588e-01
## theta[507] 1.184667e-01 1.485388e-01 1.811566e-01 2.603593e-01
## theta[508] 1.667964e-01 1.854285e-01 2.044092e-01 2.422122e-01
## theta[509] 2.468593e-01 2.585672e-01 2.694617e-01 2.948466e-01
## theta[510] 2.265507e-01 2.436327e-01 2.603494e-01 2.927931e-01
## theta[511] 9.735925e-02 1.231046e-01 1.492888e-01 2.158983e-01
## theta[512] 2.795553e-01 2.935390e-01 3.076047e-01 3.344002e-01
## theta[513] 2.316350e-01 2.453385e-01 2.600277e-01 2.932523e-01
## theta[514] 2.007560e-01 2.170955e-01 2.343490e-01 2.712821e-01
## theta[515] 9.024918e-02 1.188462e-01 1.498589e-01 2.316079e-01
## theta[516] 2.117176e-01 2.373716e-01 2.618510e-01 3.160947e-01
## theta[517] 1.824173e-01 2.028864e-01 2.262158e-01 2.760871e-01
## theta[518] 8.409802e-02 1.086139e-01 1.342828e-01 1.992860e-01
## theta[519] 9.341305e-02 1.213506e-01 1.549317e-01 2.282307e-01
## theta[520] 9.290217e-02 1.250805e-01 1.577395e-01 2.340292e-01
## theta[521] 2.220063e-01 2.349210e-01 2.501338e-01 2.769771e-01
## theta[522] 2.519638e-01 2.639879e-01 2.764774e-01 2.988166e-01
## theta[523] 2.835390e-01 2.986212e-01 3.158263e-01 3.457199e-01
## theta[524] 2.038743e-01 2.294969e-01 2.563240e-01 3.088902e-01
## theta[525] 2.111387e-01 2.232253e-01 2.352563e-01 2.581697e-01
## theta[526] 2.431637e-01 2.620662e-01 2.817989e-01 3.160556e-01
## theta[527] 2.644266e-01 2.754438e-01 2.866673e-01 3.108499e-01
## theta[528] 8.790757e-02 1.161679e-01 1.470077e-01 2.206110e-01
## theta[529] 2.178846e-01 2.289758e-01 2.387874e-01 2.609612e-01
## theta[530] 2.187605e-01 2.354481e-01 2.507023e-01 2.860150e-01
## theta[531] 2.571743e-01 2.691550e-01 2.808716e-01 3.043722e-01
## theta[532] 8.942521e-02 1.201635e-01 1.568104e-01 2.422558e-01
## theta[533] 9.383564e-02 1.155845e-01 1.394972e-01 1.903100e-01
## theta[534] 2.914481e-01 3.102167e-01 3.288184e-01 3.652755e-01
## theta[535] 2.053214e-01 2.339851e-01 2.611047e-01 3.139115e-01
## theta[536] 8.852016e-02 1.154967e-01 1.481218e-01 2.160463e-01
## theta[537] 2.264429e-01 2.390408e-01 2.511680e-01 2.743200e-01
## theta[538] 8.989371e-02 1.159803e-01 1.428912e-01 2.030972e-01
## theta[539] 2.382650e-01 2.535711e-01 2.693688e-01 3.008330e-01
## theta[540] 2.181093e-01 2.429403e-01 2.702980e-01 3.182675e-01
## theta[541] 1.961813e-01 2.241736e-01 2.519120e-01 3.086417e-01
## theta[542] 2.029340e-01 2.247166e-01 2.494456e-01 2.962672e-01
## theta[543] 1.925363e-01 2.170493e-01 2.440022e-01 2.940244e-01
## theta[544] 9.987786e-02 1.217786e-01 1.484504e-01 2.089571e-01
## theta[545] 2.251918e-01 2.549962e-01 2.865924e-01 3.558036e-01
## theta[546] 2.232838e-01 2.355264e-01 2.481832e-01 2.738235e-01
## theta[547] 2.259052e-01 2.531001e-01 2.813468e-01 3.426872e-01
## theta[548] 9.067824e-02 1.195482e-01 1.500950e-01 2.253049e-01
## theta[549] 1.066020e-01 1.305453e-01 1.570752e-01 2.084415e-01
## theta[550] 8.808283e-02 1.064488e-01 1.281877e-01 1.693147e-01
## theta[551] 9.243603e-02 1.223765e-01 1.553085e-01 2.282560e-01
## theta[552] 8.588072e-02 1.114347e-01 1.415585e-01 2.114861e-01
## theta[553] 2.479581e-01 2.588934e-01 2.702886e-01 2.943001e-01
## theta[554] 8.371238e-02 1.108035e-01 1.413254e-01 2.028317e-01
## theta[555] 2.312989e-01 2.549429e-01 2.790459e-01 3.248957e-01
## theta[556] 7.837139e-02 9.737069e-02 1.161424e-01 1.671149e-01
## theta[557] 2.097002e-01 2.359292e-01 2.645365e-01 3.248463e-01
## theta[558] 2.299832e-01 2.478554e-01 2.657993e-01 3.062332e-01
## theta[559] 2.038910e-01 2.285743e-01 2.553212e-01 3.102497e-01
## theta[560] 1.996121e-01 2.209246e-01 2.435366e-01 2.839950e-01
## theta[561] 9.245113e-02 1.194108e-01 1.522095e-01 2.322559e-01
## theta[562] 9.333300e-02 1.204518e-01 1.529231e-01 2.226517e-01
## theta[563] 2.527882e-01 2.657473e-01 2.806341e-01 3.090485e-01
## theta[564] 2.220461e-01 2.365788e-01 2.499959e-01 2.783330e-01
## theta[565] 2.374748e-01 2.665802e-01 2.953824e-01 3.548267e-01
## theta[566] 2.404753e-01 2.592783e-01 2.780053e-01 3.172058e-01
## theta[567] 2.464153e-01 2.630952e-01 2.801474e-01 3.122814e-01
## theta[568] 2.114151e-01 2.278154e-01 2.441816e-01 2.805448e-01
## theta[569] 2.310508e-01 2.437086e-01 2.569724e-01 2.817174e-01
## theta[570] 1.176339e-01 1.400053e-01 1.626067e-01 2.106476e-01
## theta[571] 1.088152e-01 1.367647e-01 1.727676e-01 2.557900e-01
## theta[572] 2.714150e-01 2.864162e-01 3.022217e-01 3.365097e-01
## theta[573] 1.789818e-01 2.035118e-01 2.287024e-01 2.829047e-01
## theta[574] 2.194577e-01 2.480073e-01 2.767991e-01 3.405493e-01
## theta[575] 9.447586e-02 1.227977e-01 1.546680e-01 2.243422e-01
## theta[576] 9.511938e-02 1.242805e-01 1.581012e-01 2.385581e-01
## theta[577] 2.128932e-01 2.298161e-01 2.459990e-01 2.760338e-01
## theta[578] 2.041545e-01 2.302134e-01 2.602164e-01 3.202382e-01
## theta[579] 9.172351e-02 1.204652e-01 1.536044e-01 2.301219e-01
## theta[580] 1.036066e-01 1.312298e-01 1.636894e-01 2.387453e-01
## theta[581] 2.043214e-01 2.299401e-01 2.560100e-01 3.096653e-01
## theta[582] 2.222837e-01 2.356498e-01 2.498407e-01 2.783963e-01
## theta[583] 2.368777e-01 2.574737e-01 2.764245e-01 3.163285e-01
## theta[584] 1.255963e-01 1.468824e-01 1.727749e-01 2.180321e-01
## theta[585] 2.401049e-01 2.550005e-01 2.697521e-01 3.014501e-01
## theta[586] 9.647348e-02 1.254638e-01 1.561308e-01 2.400227e-01
## theta[587] 2.412907e-01 2.576560e-01 2.741133e-01 3.087434e-01
## theta[588] 9.327788e-02 1.204544e-01 1.529285e-01 2.328160e-01
## theta[589] 2.022098e-01 2.312864e-01 2.611865e-01 3.248111e-01
## theta[590] 9.231090e-02 1.132811e-01 1.361648e-01 1.855673e-01
## theta[591] 2.871264e-01 2.979858e-01 3.086365e-01 3.308705e-01
## theta[592] 6.600214e-02 8.149590e-02 9.965304e-02 1.402600e-01
## theta[593] 2.021421e-01 2.246891e-01 2.462483e-01 2.913205e-01
## theta[594] 2.427309e-01 2.552465e-01 2.667985e-01 2.936870e-01
## theta[595] 2.373822e-01 2.554730e-01 2.734518e-01 3.094926e-01
## theta[596] 2.147426e-01 2.268240e-01 2.387816e-01 2.604534e-01
## theta[597] 1.179340e-01 1.450579e-01 1.789082e-01 2.522960e-01
## theta[598] 2.385246e-01 2.515870e-01 2.649267e-01 2.885776e-01
## theta[599] 2.524031e-01 2.650989e-01 2.761346e-01 2.971136e-01
## theta[600] 2.111572e-01 2.318624e-01 2.504672e-01 2.883837e-01
## theta[601] 2.409125e-01 2.586711e-01 2.766385e-01 3.087137e-01
## theta[602] 2.816920e-01 2.931795e-01 3.051108e-01 3.279564e-01
## theta[603] 2.211145e-01 2.371603e-01 2.538009e-01 2.881578e-01
## theta[604] 2.270939e-01 2.493477e-01 2.721987e-01 3.199453e-01
## theta[605] 1.372646e-01 1.597965e-01 1.823283e-01 2.294066e-01
## theta[606] 2.305124e-01 2.522209e-01 2.729111e-01 3.096259e-01
## theta[607] 9.220299e-02 1.208944e-01 1.486074e-01 2.245110e-01
## theta[608] 1.354132e-01 1.560864e-01 1.791879e-01 2.254773e-01
## theta[609] 2.655094e-01 2.813072e-01 2.981406e-01 3.264846e-01
## theta[610] 2.179775e-01 2.378209e-01 2.584515e-01 3.075386e-01
## theta[611] 2.182345e-01 2.359285e-01 2.541188e-01 2.984772e-01
## theta[612] 2.486949e-01 2.706833e-01 2.936408e-01 3.373692e-01
## theta[613] 2.005122e-01 2.179928e-01 2.348645e-01 2.699112e-01
## theta[614] 8.065860e-02 1.010007e-01 1.289753e-01 1.826155e-01
## theta[615] 2.192781e-01 2.418572e-01 2.637703e-01 3.107506e-01
## theta[616] 8.970698e-02 1.154395e-01 1.454200e-01 2.128534e-01
## theta[617] 1.474192e-01 1.792300e-01 2.115733e-01 2.850371e-01
## theta[618] 2.774886e-01 2.886023e-01 3.007508e-01 3.245542e-01
## theta[619] 2.786085e-01 2.933548e-01 3.086713e-01 3.358730e-01
## theta[620] 2.223680e-01 2.474617e-01 2.717879e-01 3.163723e-01
## theta[621] 2.131658e-01 2.326350e-01 2.550475e-01 2.982839e-01
## theta[622] 8.798673e-02 1.130991e-01 1.468466e-01 2.138224e-01
## theta[623] 1.852134e-01 2.025746e-01 2.218601e-01 2.661972e-01
## theta[624] 2.357451e-01 2.474913e-01 2.597474e-01 2.851968e-01
## theta[625] 2.315960e-01 2.433783e-01 2.559358e-01 2.801078e-01
## theta[626] 2.430338e-01 2.633052e-01 2.844959e-01 3.269750e-01
## theta[627] 9.066472e-02 1.195530e-01 1.515658e-01 2.258293e-01
## theta[628] 3.145147e-01 3.283631e-01 3.427459e-01 3.685370e-01
## theta[629] 2.316000e-01 2.593500e-01 2.907474e-01 3.547521e-01
## theta[630] 9.147102e-02 1.195431e-01 1.505083e-01 2.194245e-01
## theta[631] 2.597922e-01 2.713128e-01 2.830803e-01 3.058416e-01
## theta[632] 9.132586e-02 1.193439e-01 1.512280e-01 2.264350e-01
## theta[633] 2.711922e-01 2.826930e-01 2.952431e-01 3.179550e-01
## theta[634] 2.461010e-01 2.595695e-01 2.727941e-01 3.020816e-01
## theta[635] 1.900655e-01 2.083418e-01 2.271333e-01 2.622041e-01
## theta[636] 2.180902e-01 2.336431e-01 2.502939e-01 2.794259e-01
## theta[637] 2.368882e-01 2.485266e-01 2.599566e-01 2.826782e-01
## theta[638] 2.602249e-01 2.723419e-01 2.831213e-01 3.049634e-01
## theta[639] 8.646300e-02 1.128433e-01 1.421036e-01 1.995897e-01
## theta[640] 3.084218e-01 3.207786e-01 3.325258e-01 3.534724e-01
## theta[641] 1.970666e-01 2.138431e-01 2.320000e-01 2.663098e-01
## theta[642] 2.643441e-01 2.776947e-01 2.908290e-01 3.157731e-01
## theta[643] 2.126148e-01 2.265421e-01 2.417685e-01 2.697708e-01
## theta[644] 2.376827e-01 2.501774e-01 2.629624e-01 2.884142e-01
## theta[645] 2.422485e-01 2.605140e-01 2.786109e-01 3.156329e-01
## theta[646] 2.094306e-01 2.264249e-01 2.451813e-01 2.816816e-01
## theta[647] 1.962706e-01 2.212338e-01 2.473494e-01 3.028598e-01
## theta[648] 9.272277e-02 1.222840e-01 1.577984e-01 2.315664e-01
## theta[649] 9.125412e-02 1.127452e-01 1.356948e-01 1.906617e-01
## theta[650] 2.449085e-01 2.661420e-01 2.863393e-01 3.340429e-01
## theta[651] 1.903190e-01 2.170728e-01 2.457140e-01 3.058830e-01
## theta[652] 9.197045e-02 1.217044e-01 1.557138e-01 2.271398e-01
## theta[653] 1.979907e-01 2.204026e-01 2.447702e-01 3.003434e-01
## theta[654] 7.733568e-02 9.732210e-02 1.195681e-01 1.637436e-01
## theta[655] 2.695763e-01 2.829625e-01 2.956077e-01 3.218633e-01
## theta[656] 2.325067e-01 2.436029e-01 2.547497e-01 2.802570e-01
## theta[657] 2.160781e-01 2.290543e-01 2.434404e-01 2.688327e-01
## theta[658] 1.828574e-01 2.010989e-01 2.210951e-01 2.663284e-01
## theta[659] 2.006485e-01 2.238586e-01 2.500034e-01 3.032354e-01
## theta[660] 1.016361e-01 1.277353e-01 1.600062e-01 2.362805e-01
## theta[661] 3.039869e-01 3.164226e-01 3.286561e-01 3.527081e-01
## theta[662] 8.958044e-02 1.173522e-01 1.504028e-01 2.238176e-01
## theta[663] 2.000156e-01 2.211996e-01 2.431023e-01 2.872597e-01
## theta[664] 2.556478e-01 2.704536e-01 2.842979e-01 3.143626e-01
## theta[665] 2.195663e-01 2.381573e-01 2.579073e-01 2.965016e-01
## theta[666] 1.950006e-01 2.151578e-01 2.376537e-01 2.783099e-01
## theta[667] 2.268135e-01 2.416990e-01 2.563295e-01 2.875744e-01
## theta[668] 2.414296e-01 2.576485e-01 2.737975e-01 3.056920e-01
## theta[669] 2.062654e-01 2.336918e-01 2.634997e-01 3.172575e-01
## theta[670] 9.524753e-02 1.255196e-01 1.540569e-01 2.279590e-01
## theta[671] 9.136374e-02 1.145190e-01 1.365233e-01 1.934905e-01
## theta[672] 9.295602e-02 1.207942e-01 1.547148e-01 2.342121e-01
## theta[673] 2.618509e-01 2.744058e-01 2.872668e-01 3.100207e-01
## theta[674] 9.310438e-02 1.217039e-01 1.581391e-01 2.363325e-01
## theta[675] 2.111278e-01 2.369056e-01 2.654185e-01 3.221970e-01
## theta[676] 1.665733e-01 1.803294e-01 1.952963e-01 2.288859e-01
## theta[677] 2.085657e-01 2.317822e-01 2.558033e-01 2.941018e-01
## theta[678] 2.784119e-01 2.908159e-01 3.032390e-01 3.268751e-01
## theta[679] 2.137167e-01 2.320411e-01 2.503394e-01 2.890135e-01
## theta[680] 2.572304e-01 2.692004e-01 2.814390e-01 3.050357e-01
## theta[681] 9.372186e-02 1.217849e-01 1.559865e-01 2.414499e-01
## theta[682] 2.471094e-01 2.726281e-01 2.967994e-01 3.442241e-01
## theta[683] 2.277662e-01 2.421065e-01 2.570816e-01 2.884885e-01
## theta[684] 2.593416e-01 2.703545e-01 2.814502e-01 3.048244e-01
## theta[685] 2.288503e-01 2.449823e-01 2.618591e-01 2.984616e-01
## theta[686] 2.231765e-01 2.395597e-01 2.571506e-01 2.941962e-01
## theta[687] 1.975472e-01 2.277902e-01 2.574599e-01 3.169074e-01
## theta[688] 2.005383e-01 2.158912e-01 2.315235e-01 2.615814e-01
## theta[689] 2.660239e-01 2.798315e-01 2.924100e-01 3.175109e-01
## theta[690] 9.558756e-02 1.195917e-01 1.438711e-01 2.007929e-01
## theta[691] 2.684096e-01 2.800743e-01 2.917951e-01 3.153913e-01
## theta[692] 1.887735e-01 2.059654e-01 2.236031e-01 2.596215e-01
## theta[693] 2.791303e-01 2.910601e-01 3.034311e-01 3.260408e-01
## theta[694] 7.597671e-02 9.360165e-02 1.121850e-01 1.557392e-01
## theta[695] 2.346750e-01 2.468189e-01 2.576809e-01 2.825882e-01
## theta[696] 2.663317e-01 2.807100e-01 2.964984e-01 3.286853e-01
## theta[697] 2.104064e-01 2.282968e-01 2.486134e-01 2.870014e-01
## theta[698] 2.617879e-01 2.861767e-01 3.105484e-01 3.578397e-01
## theta[699] 2.484991e-01 2.707809e-01 2.941996e-01 3.397957e-01
## theta[700] 2.143140e-01 2.313080e-01 2.492997e-01 2.849041e-01
## theta[701] 9.233481e-02 1.212890e-01 1.533543e-01 2.316436e-01
## theta[702] 1.026786e-01 1.299362e-01 1.633285e-01 2.403893e-01
## theta[703] 2.428320e-01 2.562374e-01 2.690518e-01 2.976225e-01
## theta[704] 2.936729e-01 3.053646e-01 3.187574e-01 3.420932e-01
## theta[705] 2.401878e-01 2.544019e-01 2.693487e-01 2.951552e-01
## theta[706] 2.499936e-01 2.619484e-01 2.738249e-01 2.982908e-01
## theta[707] 2.313314e-01 2.605792e-01 2.921041e-01 3.578049e-01
## theta[708] 2.419023e-01 2.547359e-01 2.668115e-01 2.942603e-01
## theta[709] 2.192735e-01 2.488521e-01 2.781704e-01 3.416181e-01
## theta[710] 2.036518e-01 2.182710e-01 2.338453e-01 2.653428e-01
## theta[711] 1.361352e-01 1.611036e-01 1.916330e-01 2.721811e-01
## theta[712] 1.047864e-01 1.343251e-01 1.673620e-01 2.363746e-01
## theta[713] 1.132212e-01 1.353017e-01 1.601299e-01 2.201388e-01
## theta[714] 2.286198e-01 2.418394e-01 2.553538e-01 2.803160e-01
## theta[715] 2.232421e-01 2.454518e-01 2.719945e-01 3.203381e-01
## theta[716] 2.630151e-01 2.774417e-01 2.932770e-01 3.199065e-01
## theta[717] 1.876511e-01 2.159761e-01 2.457702e-01 3.037667e-01
## theta[718] 9.243853e-02 1.202344e-01 1.505559e-01 2.320981e-01
## theta[719] 9.251648e-02 1.208373e-01 1.574318e-01 2.400920e-01
## theta[720] 2.200509e-01 2.378184e-01 2.570436e-01 2.980761e-01
## theta[721] 8.916661e-02 1.172033e-01 1.506438e-01 2.271773e-01
## theta[722] 2.230854e-01 2.330413e-01 2.435151e-01 2.627221e-01
## theta[723] 1.226349e-01 1.449316e-01 1.677165e-01 2.207276e-01
## theta[724] 9.939252e-02 1.292327e-01 1.658961e-01 2.419188e-01
## theta[725] 2.412033e-01 2.623525e-01 2.847830e-01 3.277302e-01
## theta[726] 2.180865e-01 2.414358e-01 2.660459e-01 3.162263e-01
## theta[727] 9.755232e-02 1.237864e-01 1.534316e-01 2.279168e-01
## theta[728] 9.458654e-02 1.206611e-01 1.509361e-01 2.299323e-01
## theta[729] 2.066246e-01 2.191567e-01 2.309957e-01 2.531561e-01
## theta[730] 2.926595e-01 3.040603e-01 3.154507e-01 3.383734e-01
## theta[731] 2.005879e-01 2.134892e-01 2.286658e-01 2.533973e-01
## theta[732] 2.593920e-01 2.756233e-01 2.926420e-01 3.318336e-01
## theta[733] 9.581801e-02 1.240815e-01 1.601739e-01 2.407387e-01
## theta[734] 2.383944e-01 2.554671e-01 2.714897e-01 3.086946e-01
## theta[735] 2.209570e-01 2.452038e-01 2.722589e-01 3.173179e-01
## theta[736] 6.754332e-02 8.620004e-02 1.086662e-01 1.531073e-01
## theta[737] 8.841832e-02 1.124586e-01 1.362974e-01 1.973250e-01
## theta[738] 1.248297e-01 1.475111e-01 1.712809e-01 2.253952e-01
## theta[739] 2.693347e-01 2.822396e-01 2.947030e-01 3.199143e-01
## theta[740] 2.370450e-01 2.576228e-01 2.797086e-01 3.215457e-01
## theta[741] 2.036277e-01 2.154997e-01 2.270135e-01 2.501245e-01
## theta[742] 9.258938e-02 1.128994e-01 1.368747e-01 1.896012e-01
## theta[743] 2.566745e-01 2.688489e-01 2.811708e-01 3.086716e-01
## theta[744] 2.136695e-01 2.309740e-01 2.481055e-01 2.833161e-01
## theta[745] 2.522152e-01 2.660764e-01 2.815287e-01 3.104108e-01
## theta[746] 2.133186e-01 2.288340e-01 2.456017e-01 2.739112e-01
## theta[747] 2.244172e-01 2.432998e-01 2.634938e-01 3.048165e-01
## theta[748] 2.158908e-01 2.457278e-01 2.766754e-01 3.386866e-01
## theta[749] 1.709998e-01 1.878503e-01 2.046943e-01 2.363482e-01
## theta[750] 2.576683e-01 2.695159e-01 2.817343e-01 3.080986e-01
## theta[751] 9.252364e-02 1.235923e-01 1.591349e-01 2.295284e-01
## theta[752] 1.809257e-01 1.967193e-01 2.124659e-01 2.420826e-01
## theta[753] 2.256106e-01 2.374474e-01 2.500148e-01 2.756116e-01
## theta[754] 2.430130e-01 2.599070e-01 2.761206e-01 3.149638e-01
## theta[755] 2.497377e-01 2.649721e-01 2.800296e-01 3.090386e-01
## theta[756] 8.914652e-02 1.082893e-01 1.327437e-01 1.839737e-01
## theta[757] 9.513353e-02 1.240722e-01 1.568396e-01 2.331878e-01
## theta[758] 2.273270e-01 2.471616e-01 2.666645e-01 3.103614e-01
## theta[759] 2.670188e-01 2.788382e-01 2.906883e-01 3.152602e-01
## theta[760] 2.706693e-01 2.863267e-01 3.030415e-01 3.371805e-01
## theta[761] 2.340833e-01 2.557882e-01 2.766170e-01 3.174429e-01
## theta[762] 9.565212e-02 1.251334e-01 1.568024e-01 2.275538e-01
## theta[763] 2.214176e-01 2.486397e-01 2.749053e-01 3.290154e-01
## theta[764] 1.105565e-01 1.377137e-01 1.696232e-01 2.434840e-01
## theta[765] 1.902537e-01 2.107240e-01 2.323439e-01 2.767755e-01
## theta[766] 9.837629e-02 1.244463e-01 1.573724e-01 2.382825e-01
## theta[767] 1.040925e-01 1.308136e-01 1.628649e-01 2.423349e-01
## theta[768] 2.473743e-01 2.595105e-01 2.719104e-01 2.983506e-01
## theta[769] 9.205411e-02 1.222937e-01 1.531025e-01 2.225649e-01
## theta[770] 2.403991e-01 2.567867e-01 2.736109e-01 3.063478e-01
## theta[771] 2.631986e-01 2.801240e-01 2.970095e-01 3.343731e-01
## theta[772] 2.325823e-01 2.469797e-01 2.622131e-01 2.918982e-01
## theta[773] 2.030095e-01 2.260579e-01 2.507690e-01 2.949967e-01
## theta[774] 2.045170e-01 2.318963e-01 2.601958e-01 3.188902e-01
## theta[775] 2.089824e-01 2.221556e-01 2.363898e-01 2.654378e-01
## theta[776] 2.285631e-01 2.421178e-01 2.544426e-01 2.788100e-01
## theta[777] 9.328519e-02 1.223030e-01 1.590437e-01 2.450998e-01
## theta[778] 2.340217e-01 2.528526e-01 2.710900e-01 3.088411e-01
## theta[779] 2.437312e-01 2.553207e-01 2.677562e-01 2.897778e-01
## theta[780] 9.326067e-02 1.151398e-01 1.402431e-01 1.966835e-01
## theta[781] 1.242015e-01 1.582191e-01 1.938309e-01 2.838356e-01
## theta[782] 2.040737e-01 2.171594e-01 2.305127e-01 2.629696e-01
## theta[783] 2.531397e-01 2.676350e-01 2.831529e-01 3.142592e-01
## theta[784] 2.675567e-01 2.795555e-01 2.909062e-01 3.142917e-01
## theta[785] 2.353974e-01 2.535593e-01 2.724391e-01 3.057284e-01
## theta[786] 2.138327e-01 2.286697e-01 2.454654e-01 2.751193e-01
## theta[787] 1.151217e-01 1.459873e-01 1.769046e-01 2.543100e-01
## theta[788] 1.708481e-01 1.987414e-01 2.276925e-01 2.889406e-01
## theta[789] 1.606153e-01 1.862652e-01 2.086510e-01 2.596405e-01
## theta[790] 9.314558e-02 1.219661e-01 1.559585e-01 2.264747e-01
## theta[791] 1.966404e-01 2.119231e-01 2.276128e-01 2.635247e-01
## theta[792] 9.426813e-02 1.222325e-01 1.544973e-01 2.248738e-01
## theta[793] 2.255104e-01 2.432717e-01 2.602704e-01 2.924381e-01
## theta[794] 2.196822e-01 2.459445e-01 2.719470e-01 3.292202e-01
## theta[795] 2.046864e-01 2.344654e-01 2.632360e-01 3.224264e-01
## theta[796] 1.962016e-01 2.200802e-01 2.444164e-01 2.979078e-01
## theta[797] 1.967005e-01 2.165523e-01 2.369412e-01 2.761424e-01
## theta[798] 1.819420e-01 2.059756e-01 2.307493e-01 2.780353e-01
## theta[799] 8.464511e-02 1.102838e-01 1.408474e-01 2.130154e-01
## theta[800] 2.138479e-01 2.431316e-01 2.740071e-01 3.312475e-01
## theta[801] 2.202158e-01 2.432131e-01 2.687751e-01 3.218937e-01
## theta[802] 9.161174e-02 1.209062e-01 1.558232e-01 2.291713e-01
## theta[803] 2.116510e-01 2.409015e-01 2.724921e-01 3.454181e-01
## theta[804] 1.493938e-01 1.705380e-01 1.957185e-01 2.498800e-01
## theta[805] 8.654079e-02 1.059709e-01 1.301805e-01 1.722133e-01
## theta[806] 9.755208e-02 1.240520e-01 1.544008e-01 2.316874e-01
## theta[807] 2.560880e-01 2.690069e-01 2.817986e-01 3.061751e-01
## theta[808] 2.269413e-01 2.418606e-01 2.565128e-01 2.848842e-01
## theta[809] 9.583629e-02 1.255708e-01 1.530378e-01 2.256692e-01
## theta[810] 1.186408e-01 1.477340e-01 1.836822e-01 2.623349e-01
## theta[811] 9.451561e-02 1.245718e-01 1.606031e-01 2.333780e-01
## theta[812] 5.494413e-02 7.170563e-02 9.386554e-02 1.345115e-01
## theta[813] 9.275114e-02 1.222776e-01 1.558136e-01 2.405167e-01
## theta[814] 1.038444e-01 1.343598e-01 1.645797e-01 2.407050e-01
## theta[815] 2.310022e-01 2.531938e-01 2.768191e-01 3.254432e-01
## theta[816] 2.431182e-01 2.609085e-01 2.792648e-01 3.147926e-01
## theta[817] 9.386588e-02 1.212363e-01 1.527590e-01 2.372973e-01
## theta[818] 2.279050e-01 2.466311e-01 2.669022e-01 3.066089e-01
## theta[819] 9.478132e-02 1.242437e-01 1.564724e-01 2.317038e-01
## theta[820] 2.909258e-01 3.032248e-01 3.156700e-01 3.409903e-01
## theta[821] 9.051843e-02 1.159958e-01 1.493273e-01 2.270352e-01
## theta[822] 2.151710e-01 2.360997e-01 2.569894e-01 3.006067e-01
## theta[823] 2.344971e-01 2.528053e-01 2.733204e-01 3.117681e-01
## theta[824] 2.371856e-01 2.550972e-01 2.733793e-01 3.094053e-01
## theta[825] 1.322592e-01 1.550779e-01 1.819123e-01 2.307954e-01
## theta[826] 2.158235e-01 2.316057e-01 2.492746e-01 2.867260e-01
## theta[827] 8.913718e-02 1.149163e-01 1.472003e-01 2.137907e-01
## theta[828] 1.044042e-01 1.231710e-01 1.429830e-01 1.836984e-01
## theta[829] 2.246465e-01 2.371409e-01 2.501403e-01 2.750805e-01
## theta[830] 2.540122e-01 2.734287e-01 2.921546e-01 3.281834e-01
## theta[831] 1.916767e-01 2.170968e-01 2.429429e-01 2.983943e-01
## theta[832] 2.243259e-01 2.391260e-01 2.533363e-01 2.821922e-01
## theta[833] 1.252604e-01 1.521638e-01 1.863315e-01 2.516798e-01
## theta[834] 9.151389e-02 1.160655e-01 1.459122e-01 2.211080e-01
## theta[835] 2.692232e-01 2.827785e-01 2.965919e-01 3.244555e-01
## theta[836] 2.051988e-01 2.244735e-01 2.435481e-01 2.836660e-01
## theta[837] 2.182926e-01 2.485396e-01 2.801648e-01 3.521244e-01
## theta[838] 2.199457e-01 2.335710e-01 2.470838e-01 2.756685e-01
## theta[839] 2.390879e-01 2.564141e-01 2.743985e-01 3.100286e-01
## theta[840] 2.261688e-01 2.437812e-01 2.612926e-01 2.945173e-01
## theta[841] 8.246224e-02 1.095830e-01 1.382613e-01 2.005222e-01
## theta[842] 1.039744e-01 1.310376e-01 1.634143e-01 2.415678e-01
## theta[843] 9.252893e-02 1.210079e-01 1.565567e-01 2.309130e-01
## theta[844] 8.522194e-02 1.120202e-01 1.425392e-01 2.132128e-01
## theta[845] 8.924393e-02 1.098543e-01 1.326470e-01 1.830347e-01
## theta[846] 2.194296e-01 2.353208e-01 2.521032e-01 2.867276e-01
## theta[847] 9.531378e-02 1.239816e-01 1.566807e-01 2.419429e-01
## theta[848] 1.222457e-01 1.527896e-01 1.893003e-01 2.750456e-01
## theta[849] 1.884911e-01 2.106504e-01 2.331625e-01 2.743728e-01
## theta[850] 1.093412e-01 1.392362e-01 1.714062e-01 2.498836e-01
## theta[851] 9.049648e-02 1.158574e-01 1.443325e-01 2.108258e-01
## theta[852] 1.286766e-01 1.486213e-01 1.732281e-01 2.224655e-01
## theta[853] 7.492646e-02 9.244815e-02 1.114731e-01 1.497177e-01
## theta[854] 2.370434e-01 2.551329e-01 2.736894e-01 3.099024e-01
## theta[855] 9.171802e-02 1.197878e-01 1.522724e-01 2.249262e-01
## theta[856] 2.424102e-01 2.646298e-01 2.865382e-01 3.334550e-01
## theta[857] 2.518431e-01 2.638919e-01 2.767983e-01 3.023645e-01
## theta[858] 2.636544e-01 2.785279e-01 2.942784e-01 3.244562e-01
## theta[859] 2.172133e-01 2.365426e-01 2.553452e-01 2.949466e-01
## theta[860] 2.494083e-01 2.607094e-01 2.744388e-01 2.979377e-01
## theta[861] 2.751059e-01 2.902774e-01 3.072909e-01 3.355682e-01
## theta[862] 1.865474e-01 2.079634e-01 2.318041e-01 2.823878e-01
## theta[863] 2.449896e-01 2.597553e-01 2.742952e-01 3.039436e-01
## theta[864] 2.326946e-01 2.534046e-01 2.770315e-01 3.203076e-01
## theta[865] 2.023370e-01 2.180182e-01 2.336752e-01 2.676826e-01
## theta[866] 9.702965e-02 1.243338e-01 1.536051e-01 2.213250e-01
## theta[867] 2.152160e-01 2.354186e-01 2.572022e-01 2.985861e-01
## theta[868] 9.371068e-02 1.209804e-01 1.549307e-01 2.332120e-01
## theta[869] 1.932223e-01 2.099189e-01 2.285524e-01 2.619913e-01
## theta[870] 2.558857e-01 2.758562e-01 2.990314e-01 3.455315e-01
## theta[871] 2.911133e-01 3.026325e-01 3.139268e-01 3.371201e-01
## theta[872] 1.999965e-01 2.198741e-01 2.423147e-01 2.875620e-01
## theta[873] 2.064952e-01 2.257135e-01 2.481636e-01 2.870275e-01
## theta[874] 2.632720e-01 2.782862e-01 2.964625e-01 3.302758e-01
## theta[875] 2.718421e-01 2.849614e-01 2.972243e-01 3.226322e-01
## theta[876] 2.575442e-01 2.691512e-01 2.809597e-01 3.047044e-01
## theta[877] 2.118433e-01 2.297985e-01 2.470217e-01 2.838089e-01
## theta[878] 1.255586e-01 1.463438e-01 1.687952e-01 2.163407e-01
## theta[879] 1.085097e-01 1.373138e-01 1.735058e-01 2.477623e-01
## theta[880] 2.407317e-01 2.532159e-01 2.650215e-01 2.873941e-01
## theta[881] 2.195460e-01 2.346206e-01 2.513170e-01 2.809183e-01
## theta[882] 9.867440e-02 1.298474e-01 1.632581e-01 2.428744e-01
## theta[883] 9.384512e-02 1.212092e-01 1.531619e-01 2.278629e-01
## theta[884] 2.089078e-01 2.364189e-01 2.653110e-01 3.203563e-01
## theta[885] 2.359801e-01 2.456917e-01 2.568592e-01 2.794541e-01
## theta[886] 1.334036e-01 1.589956e-01 1.868534e-01 2.497724e-01
## gamma[1] -1.114795e+00 -1.091210e+00 -1.068956e+00 -1.028160e+00
## gamma[2] -1.119597e+00 -1.094816e+00 -1.068414e+00 -1.019457e+00
## gamma[3] -1.092785e+00 -1.069736e+00 -1.045932e+00 -1.002713e+00
## gamma[4] -1.193967e+00 -1.169522e+00 -1.145137e+00 -1.097663e+00
## gamma[5] -1.078705e+00 -1.050635e+00 -1.025012e+00 -9.746092e-01
## gamma[6] -1.125385e+00 -1.106144e+00 -1.085322e+00 -1.047092e+00
## gamma[7] -1.940331e+00 -1.903977e+00 -1.863608e+00 -1.795247e+00
## gamma[8] -1.082266e+00 -1.055410e+00 -1.029955e+00 -9.825748e-01
## gamma[9] -1.131067e+00 -1.102680e+00 -1.074293e+00 -1.018718e+00
## alpha_w 7.730640e-03 1.921883e-02 3.082921e-02 5.462162e-02
## alpha_h -2.101123e-02 -8.964544e-03 2.253103e-03 2.381179e-02
## kappa[1] 9.152224e+01 1.057265e+02 1.212664e+02 1.549651e+02
## kappa[2] 8.775417e+01 1.033454e+02 1.210196e+02 1.533118e+02
## kappa[3] 8.144652e+01 9.456150e+01 1.092166e+02 1.493394e+02
## kappa[4] 7.798249e+01 9.056660e+01 1.033270e+02 1.305335e+02
## kappa[5] 7.694531e+01 9.181118e+01 1.074441e+02 1.443827e+02
## kappa[6] 9.149713e+01 1.057869e+02 1.207607e+02 1.609470e+02
## kappa[7] 4.277656e+01 5.090627e+01 6.043860e+01 8.529693e+01
## kappa[8] 9.075114e+01 1.065352e+02 1.250055e+02 1.699696e+02
## kappa[9] 7.459716e+01 8.753801e+01 1.032568e+02 1.422555e+02
## lp__ -8.743109e+04 -8.740500e+04 -8.737897e+04 -8.733117e+04
## n_eff Rhat
## theta[1] 1500.0000 0.9982821
## theta[2] 1500.0000 0.9988329
## theta[3] 1500.0000 0.9990184
## theta[4] 1500.0000 0.9985134
## theta[5] 1500.0000 0.9986235
## theta[6] 1500.0000 0.9991443
## theta[7] 1500.0000 0.9987953
## theta[8] 1500.0000 0.9999555
## theta[9] 1500.0000 0.9985165
## theta[10] 1500.0000 0.9996852
## theta[11] 1500.0000 0.9994424
## theta[12] 1500.0000 0.9983514
## theta[13] 1500.0000 0.9986811
## theta[14] 1500.0000 0.9989519
## theta[15] 1500.0000 0.9984948
## theta[16] 1500.0000 0.9999487
## theta[17] 1500.0000 0.9982981
## theta[18] 1500.0000 0.9987649
## theta[19] 1500.0000 1.0003631
## theta[20] 1500.0000 0.9985579
## theta[21] 1500.0000 1.0002765
## theta[22] 1500.0000 0.9991781
## theta[23] 1500.0000 1.0023442
## theta[24] 1500.0000 0.9982913
## theta[25] 1500.0000 1.0002835
## theta[26] 1500.0000 0.9982989
## theta[27] 1500.0000 0.9983732
## theta[28] 1500.0000 0.9984448
## theta[29] 1500.0000 0.9993752
## theta[30] 1500.0000 1.0001005
## theta[31] 1500.0000 0.9987790
## theta[32] 1500.0000 0.9995108
## theta[33] 1500.0000 0.9983607
## theta[34] 1500.0000 0.9981503
## theta[35] 1500.0000 0.9988706
## theta[36] 1500.0000 0.9988622
## theta[37] 1500.0000 0.9981770
## theta[38] 1500.0000 0.9990789
## theta[39] 1500.0000 0.9988400
## theta[40] 1500.0000 0.9981139
## theta[41] 1500.0000 0.9988222
## theta[42] 1500.0000 0.9999594
## theta[43] 1500.0000 0.9990978
## theta[44] 1500.0000 0.9985772
## theta[45] 1500.0000 0.9995969
## theta[46] 1500.0000 0.9983276
## theta[47] 1500.0000 0.9989360
## theta[48] 1500.0000 0.9981827
## theta[49] 1500.0000 0.9989129
## theta[50] 1500.0000 0.9988653
## theta[51] 1500.0000 0.9986938
## theta[52] 1500.0000 0.9986969
## theta[53] 1500.0000 0.9984451
## theta[54] 1500.0000 0.9989315
## theta[55] 1500.0000 1.0010010
## theta[56] 1500.0000 0.9993708
## theta[57] 1500.0000 0.9983612
## theta[58] 1500.0000 1.0013911
## theta[59] 1500.0000 0.9982948
## theta[60] 1500.0000 0.9984862
## theta[61] 1500.0000 0.9984180
## theta[62] 1500.0000 0.9992056
## theta[63] 1500.0000 1.0005362
## theta[64] 1500.0000 0.9985877
## theta[65] 1500.0000 0.9984368
## theta[66] 1500.0000 1.0001181
## theta[67] 1500.0000 0.9985806
## theta[68] 1500.0000 0.9990213
## theta[69] 1500.0000 0.9988730
## theta[70] 1500.0000 0.9997707
## theta[71] 1500.0000 0.9985600
## theta[72] 1500.0000 1.0000257
## theta[73] 1500.0000 0.9998629
## theta[74] 1500.0000 1.0003848
## theta[75] 1500.0000 1.0002363
## theta[76] 1500.0000 0.9986384
## theta[77] 1500.0000 0.9997927
## theta[78] 1500.0000 0.9988500
## theta[79] 1500.0000 0.9992268
## theta[80] 1500.0000 0.9988579
## theta[81] 1500.0000 0.9985818
## theta[82] 1500.0000 0.9984444
## theta[83] 1500.0000 1.0001811
## theta[84] 1500.0000 0.9987079
## theta[85] 1500.0000 0.9997824
## theta[86] 1500.0000 0.9989717
## theta[87] 1500.0000 0.9988724
## theta[88] 1500.0000 1.0005251
## theta[89] 1500.0000 0.9984744
## theta[90] 1500.0000 1.0005499
## theta[91] 1500.0000 0.9988687
## theta[92] 1500.0000 0.9992905
## theta[93] 1500.0000 0.9987719
## theta[94] 1500.0000 0.9990418
## theta[95] 1500.0000 0.9983412
## theta[96] 1500.0000 0.9996885
## theta[97] 1500.0000 0.9987288
## theta[98] 1500.0000 0.9982689
## theta[99] 1500.0000 1.0014976
## theta[100] 1500.0000 0.9993570
## theta[101] 1500.0000 0.9994262
## theta[102] 1500.0000 0.9991613
## theta[103] 1500.0000 0.9983455
## theta[104] 1500.0000 0.9992485
## theta[105] 1500.0000 0.9986658
## theta[106] 1500.0000 0.9993447
## theta[107] 1500.0000 0.9989316
## theta[108] 1500.0000 1.0001653
## theta[109] 1500.0000 0.9992385
## theta[110] 1500.0000 0.9988910
## theta[111] 1500.0000 0.9984700
## theta[112] 1500.0000 0.9987320
## theta[113] 1500.0000 1.0003320
## theta[114] 1500.0000 0.9984544
## theta[115] 1500.0000 0.9982919
## theta[116] 1500.0000 0.9984721
## theta[117] 1500.0000 0.9988574
## theta[118] 1500.0000 0.9992502
## theta[119] 1500.0000 0.9988638
## theta[120] 1500.0000 0.9991587
## theta[121] 1500.0000 1.0009514
## theta[122] 1500.0000 0.9981839
## theta[123] 1500.0000 0.9995510
## theta[124] 1500.0000 0.9996904
## theta[125] 1500.0000 0.9988052
## theta[126] 1500.0000 0.9993354
## theta[127] 1500.0000 0.9981539
## theta[128] 1500.0000 0.9987937
## theta[129] 1500.0000 0.9997624
## theta[130] 1500.0000 1.0001785
## theta[131] 1500.0000 0.9997793
## theta[132] 1500.0000 0.9984343
## theta[133] 1500.0000 0.9991880
## theta[134] 1500.0000 0.9995764
## theta[135] 1500.0000 0.9991859
## theta[136] 1500.0000 0.9993975
## theta[137] 1500.0000 0.9996006
## theta[138] 1500.0000 1.0007870
## theta[139] 1500.0000 0.9994295
## theta[140] 1500.0000 0.9984929
## theta[141] 1500.0000 0.9983262
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## theta[688] 1500.0000 0.9987057
## theta[689] 1500.0000 0.9988496
## theta[690] 1500.0000 0.9991551
## theta[691] 1500.0000 0.9988078
## theta[692] 1500.0000 0.9983106
## theta[693] 1500.0000 0.9984227
## theta[694] 1500.0000 0.9995083
## theta[695] 1500.0000 0.9986273
## theta[696] 1500.0000 0.9992830
## theta[697] 1500.0000 0.9997030
## theta[698] 1500.0000 0.9997671
## theta[699] 1500.0000 1.0003149
## theta[700] 1500.0000 0.9983741
## theta[701] 1500.0000 0.9993811
## theta[702] 1500.0000 0.9985778
## theta[703] 1500.0000 0.9992577
## theta[704] 1500.0000 0.9984699
## theta[705] 1500.0000 0.9999798
## theta[706] 1500.0000 0.9992941
## theta[707] 1500.0000 0.9982337
## theta[708] 1500.0000 0.9993919
## theta[709] 1500.0000 1.0007853
## theta[710] 1500.0000 0.9987036
## theta[711] 1500.0000 0.9986128
## theta[712] 1500.0000 0.9988982
## theta[713] 1500.0000 0.9984091
## theta[714] 1500.0000 0.9991562
## theta[715] 1500.0000 0.9993582
## theta[716] 1500.0000 0.9993556
## theta[717] 1500.0000 0.9991021
## theta[718] 1500.0000 0.9988413
## theta[719] 1500.0000 0.9988405
## theta[720] 1500.0000 0.9983089
## theta[721] 1500.0000 0.9998038
## theta[722] 1500.0000 0.9988017
## theta[723] 1500.0000 0.9990086
## theta[724] 1500.0000 0.9987351
## theta[725] 1500.0000 0.9990264
## theta[726] 1500.0000 0.9981954
## theta[727] 1500.0000 0.9990610
## theta[728] 1500.0000 0.9999288
## theta[729] 1500.0000 0.9994143
## theta[730] 1500.0000 0.9994607
## theta[731] 1500.0000 0.9986717
## theta[732] 1500.0000 1.0006318
## theta[733] 1500.0000 0.9985981
## theta[734] 1500.0000 0.9994685
## theta[735] 1500.0000 1.0024417
## theta[736] 1500.0000 0.9995309
## theta[737] 1500.0000 0.9990438
## theta[738] 1500.0000 0.9981556
## theta[739] 1500.0000 0.9988539
## theta[740] 1500.0000 0.9987005
## theta[741] 1500.0000 0.9994770
## theta[742] 1500.0000 1.0007426
## theta[743] 1500.0000 0.9989406
## theta[744] 1500.0000 0.9987049
## theta[745] 1500.0000 0.9992853
## theta[746] 1500.0000 0.9983550
## theta[747] 1500.0000 0.9988534
## theta[748] 1500.0000 0.9988841
## theta[749] 1500.0000 0.9991924
## theta[750] 1500.0000 0.9986152
## theta[751] 1500.0000 0.9985828
## theta[752] 1500.0000 0.9998213
## theta[753] 1500.0000 0.9986438
## theta[754] 1500.0000 0.9985736
## theta[755] 1500.0000 0.9995773
## theta[756] 1500.0000 0.9988246
## theta[757] 1500.0000 0.9987866
## theta[758] 1500.0000 0.9989866
## theta[759] 1500.0000 0.9981263
## theta[760] 1500.0000 0.9989577
## theta[761] 1500.0000 0.9983183
## theta[762] 1500.0000 1.0014060
## theta[763] 1500.0000 0.9989811
## theta[764] 1500.0000 0.9988949
## theta[765] 1500.0000 0.9991807
## theta[766] 1500.0000 0.9993236
## theta[767] 1500.0000 0.9989371
## theta[768] 1500.0000 0.9982738
## theta[769] 1500.0000 1.0001340
## theta[770] 1500.0000 1.0005707
## theta[771] 1500.0000 0.9995444
## theta[772] 1500.0000 0.9984104
## theta[773] 1500.0000 1.0007827
## theta[774] 1500.0000 0.9985670
## theta[775] 1500.0000 0.9992201
## theta[776] 1500.0000 0.9987471
## theta[777] 1500.0000 0.9983016
## theta[778] 1500.0000 0.9994140
## theta[779] 1500.0000 0.9985543
## theta[780] 1500.0000 0.9994931
## theta[781] 1500.0000 0.9985199
## theta[782] 1500.0000 1.0007742
## theta[783] 1500.0000 0.9980983
## theta[784] 1500.0000 0.9987136
## theta[785] 1500.0000 0.9990211
## theta[786] 1500.0000 1.0003746
## theta[787] 1500.0000 1.0009944
## theta[788] 1500.0000 0.9988307
## theta[789] 1500.0000 0.9988881
## theta[790] 1500.0000 0.9991574
## theta[791] 1500.0000 0.9991365
## theta[792] 1500.0000 0.9990787
## theta[793] 1500.0000 0.9986416
## theta[794] 1500.0000 0.9997475
## theta[795] 1500.0000 0.9989605
## theta[796] 1500.0000 0.9991701
## theta[797] 1500.0000 0.9989642
## theta[798] 1500.0000 0.9985014
## theta[799] 1500.0000 1.0005598
## theta[800] 1500.0000 0.9987467
## theta[801] 1500.0000 1.0001989
## theta[802] 1500.0000 1.0002035
## theta[803] 1500.0000 0.9987637
## theta[804] 1500.0000 0.9985566
## theta[805] 1500.0000 0.9994092
## theta[806] 1500.0000 0.9989189
## theta[807] 1500.0000 0.9997921
## theta[808] 1500.0000 0.9985342
## theta[809] 1500.0000 0.9982511
## theta[810] 1500.0000 0.9990002
## theta[811] 1500.0000 0.9992294
## theta[812] 1500.0000 1.0028781
## theta[813] 1500.0000 0.9995496
## theta[814] 1500.0000 0.9995942
## theta[815] 1500.0000 1.0013988
## theta[816] 1500.0000 0.9986834
## theta[817] 1500.0000 0.9986727
## theta[818] 1500.0000 0.9983087
## theta[819] 1500.0000 0.9988521
## theta[820] 1500.0000 0.9985780
## theta[821] 1500.0000 1.0013738
## theta[822] 1500.0000 0.9998492
## theta[823] 1500.0000 0.9983081
## theta[824] 1500.0000 1.0003391
## theta[825] 1500.0000 0.9986811
## theta[826] 1500.0000 0.9984155
## theta[827] 1500.0000 1.0002239
## theta[828] 1500.0000 0.9998638
## theta[829] 1500.0000 0.9992496
## theta[830] 1500.0000 1.0010346
## theta[831] 1500.0000 0.9982831
## theta[832] 1500.0000 0.9988573
## theta[833] 1500.0000 0.9982175
## theta[834] 1500.0000 0.9987459
## theta[835] 1500.0000 0.9992043
## theta[836] 1500.0000 0.9984583
## theta[837] 1500.0000 0.9999972
## theta[838] 1500.0000 0.9992345
## theta[839] 1500.0000 0.9983532
## theta[840] 1500.0000 0.9998050
## theta[841] 1500.0000 1.0000763
## theta[842] 1500.0000 0.9993824
## theta[843] 1500.0000 1.0002755
## theta[844] 1500.0000 0.9989693
## theta[845] 1500.0000 0.9985270
## theta[846] 1500.0000 0.9993703
## theta[847] 1500.0000 0.9990032
## theta[848] 1500.0000 0.9988866
## theta[849] 1500.0000 0.9993875
## theta[850] 1500.0000 0.9987081
## theta[851] 1500.0000 0.9994557
## theta[852] 1500.0000 0.9998700
## theta[853] 1500.0000 1.0002622
## theta[854] 1500.0000 1.0000921
## theta[855] 1500.0000 0.9988819
## theta[856] 1500.0000 0.9991049
## theta[857] 1500.0000 0.9985487
## theta[858] 1500.0000 1.0017424
## theta[859] 1500.0000 0.9992710
## theta[860] 1500.0000 0.9987859
## theta[861] 1500.0000 0.9982178
## theta[862] 1500.0000 0.9980837
## theta[863] 1500.0000 0.9986375
## theta[864] 1500.0000 0.9987064
## theta[865] 1500.0000 0.9996958
## theta[866] 1500.0000 1.0003499
## theta[867] 1500.0000 0.9985379
## theta[868] 1500.0000 0.9992966
## theta[869] 1500.0000 0.9990482
## theta[870] 1500.0000 1.0019095
## theta[871] 1500.0000 1.0012791
## theta[872] 1500.0000 1.0004741
## theta[873] 1500.0000 0.9981346
## theta[874] 1500.0000 0.9994480
## theta[875] 1500.0000 1.0005555
## theta[876] 1500.0000 0.9989597
## theta[877] 1500.0000 0.9985146
## theta[878] 1500.0000 0.9990253
## theta[879] 1500.0000 0.9993539
## theta[880] 1500.0000 1.0015174
## theta[881] 1500.0000 0.9989096
## theta[882] 1500.0000 0.9982438
## theta[883] 1500.0000 1.0013164
## theta[884] 1500.0000 0.9982749
## theta[885] 1500.0000 0.9990036
## theta[886] 1500.0000 0.9990837
## gamma[1] 1500.0000 0.9985502
## gamma[2] 1500.0000 0.9997498
## gamma[3] 1500.0000 0.9987605
## gamma[4] 1500.0000 1.0003365
## gamma[5] 1500.0000 0.9981247
## gamma[6] 1500.0000 0.9994714
## gamma[7] 426.6337 1.0021095
## gamma[8] 1500.0000 1.0037962
## gamma[9] 1500.0000 0.9991966
## alpha_w 1037.3963 1.0059208
## alpha_h 775.3465 1.0037133
## kappa[1] 973.1725 0.9986272
## kappa[2] 1500.0000 1.0006688
## kappa[3] 1500.0000 1.0019917
## kappa[4] 846.3462 1.0021568
## kappa[5] 1500.0000 1.0015970
## kappa[6] 846.3399 1.0027263
## kappa[7] 114.9586 1.0191766
## kappa[8] 1500.0000 0.9987328
## kappa[9] 1500.0000 1.0003157
## lp__ 121.2893 1.0125000Pitchers still don’t bat well
## ci_level: 0.8 (80% intervals)## outer_level: 0.95 (95% intervals)
Recall the mean of \(\theta_i\) is \[\begin{aligned} \mu_i = \frac{1}{1 + \exp(-\gamma_{p_i} - \alpha_h h_i - \alpha_w w_i)} . \end{aligned}\]
gamma_samples <- rstan::extract(logistic_fit)$gamma
colnames(gamma_samples) <- levels(batplus$PriPos)
mu_samples <- 1/(1+exp(-gamma_samples))
boxplot(mu_samples, ylab="posterior distrn, mean batting avg", las=3)
No effect of height or weight
## ci_level: 0.8 (80% intervals)## outer_level: 0.95 (95% intervals)
Same \(\theta\) as before?
new_post_theta <- colMeans(rstan::extract(logistic_fit)$theta)
old_post_theta <- batting$post_mean[match(batplus$Player, batting$Player)]
plot(old_post_theta, new_post_theta, xlab="theta, model 1", ylab="theta, model 2")
abline(0,1, col='red')
Conclusions
We don’t have good evidence that batting average varies substantially with height or weight.
Changing the model from a Beta prior on class means to a logistic transform of a linear model did not substantially affect the results.