Prerequisites: Biostat 602, Biostat 650 and Biostat 651
Description: Introduction to Bayesian Inference. Bayesian large sample inference, relationship with maximum likelihood. Choice of model, including prior distribution. Bayesian approaches to regression generalized linear models, categorical data, and hierarchical models. Empirical Bayes methods. Comparison with frequentist methods. Bayesian computational methods. Assessment of sensitivity to model assumptions. Emphasis on biomedical applications.
Description: Regression models for the analysis of categorical data: logistic, probit and complementary log-log models for binomial random variables; log-linear models for cross-classifications of counts; regression models for Poisson rates; and multinomial response models for both nominal and ordinal responses. Model specification and interpretation are emphasized, and model criticism, model selection.
Advisory Prerequisites: Biostatistics 682 or an equivalent course covering the basic Bayesian methods and theory. Previous experience in programming in R or C/C++ is required.
Description: This course focuses on advanced Bayesian theory and nonparametric Bayes methods including Gaussian processes, Dirichlet processes, deep neural networks, variable selection, and shrinkage priors, along with modern posterior computation algorithms including gradient based Markov chain Monte Carlo and variational Bayesian methods.
Learning Objectives: This course focuses on the advanced Bayesian inference methods including modeling, theory and computation. The target audience is the PhD candidates in Biostatistics who are interested in working on their research topics related to Bayesian statistics. R and C++ will be used for illustrations and practices.
