\[ %% % Add your macros here; they'll be included in pdf and html output. %% \newcommand{\R}{\mathbb{R}} % reals \newcommand{\E}{\mathbb{E}} % expectation \renewcommand{\P}{\mathbb{P}} % probability \DeclareMathOperator{\logit}{logit} \DeclareMathOperator{\logistic}{logistic} \DeclareMathOperator{\sd}{sd} \DeclareMathOperator{\var}{var} \DeclareMathOperator{\cov}{cov} \DeclareMathOperator{\Normal}{Normal} \DeclareMathOperator{\Poisson}{Poisson} \DeclareMathOperator{\Beta}{Beta} \DeclareMathOperator{\Binom}{Binomial} \DeclareMathOperator{\Gam}{Gamma} \DeclareMathOperator{\Exp}{Exponential} \DeclareMathOperator{\Cauchy}{Cauchy} \DeclareMathOperator{\Unif}{Unif} \DeclareMathOperator{\Dirichlet}{Dirichlet} \newcommand{\given}{\;\vert\;} \]

Schedule :: Advanced Biological Statistics II: Bio 610, Winter 2018

Peter Ralph

9 January 2018

Course schedule

The tentative schedule (subject to adjustment, especially towards the end) is (K referes to Kruschke):

Week 1 (1/9)

(slides) Recap of probability and likelihood; central limit theorem (\(\sqrt{n}\)); Bayes’ rule. The beta-binomial distribution: putting a prior on the probability of success. (K ch. 4, 5, 6)

Week 2 (1/16)

(slides) Introduction to MCMC and Stan for sampling from posterior distributions, hierarchical models for binary responses, shrinkage. (K ch. 7, 9 and Intro to Stan)

Week 3 (1/23)

(slides) Assessing power, model choice, and using simulation: looking more at shrinkage, posterior predictive sampling, model comparison. Logistic regression: robustly, including categorical factors. (K ch 13 and 21, with a bit of chapters 10-12)

Week 4 (1/30)

(slides) Assessing power, model choice, and using simulation: looking more at shrinkage,

Count data: using Poisson regression and hierarchical modeling to fit overdispersion. Model selection by crossvalidation. (K ch 24)

Week 5 (2/6)

(slides) Continuous (“metric”) data: groupwise means, univariate regression, robust regression by adjusting the noise distribution, friends of ANOVA. (K ch 16, 17, 18)

Week 6 (2/13)

(slides) Sparsifying priors and variable selection. An in-depth applied example, cumulative. (K ch 19, 20)

Week 7 (2/20)

(slides) Optimization and variational Bayes in Stan. Review of model building.

Week 8 (2/27)

(slides) Clustering and categorization: nonnegative matrix factorization. Also: t-SNE in Stan.

Week 9 (3/6)

(slides) Time series: modeling local dependency, smoothing. Conditional independence.

Week 10 (3/13)

(slides) Spatial and network covariance: sharing power between related locations. Priors to constrain visualization (e.g., regularized PCA).

And, finally: a review.