Course Description
The theory and methodology of Bayesian statistical inference. Training in statistical modeling and data analysis under the Bayesian paradigm.
Athena Title
Bayesian Stat Method with App
Prerequisite
STAT 6820 and STAT 8260 and STAT 8060
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
The goal of this course is to provide graduate audiences-- statisticians and scientists alike--an understanding of the philosophical, methodological, and computational underpinnings of Bayesian statistical inference and its methodological applications. By the end of the course, students should be able to fully specify the components of a Bayesian model (likelihood, priors, hyperpriors), obtain the optimal Bayes rule for a specified loss function, and carry out the requisite computations for the analysis of such a model. Students will know conjugate Bayesian methods, objective Bayesian methods under diffuse and improper priors, and propriety of resulting posterior distributions. Students will learn Bayesian solutions to interval estimation, hypothesis testing, and model selection problems; hierarchical Bayes or multi-level modeling; robust Bayesian methods; and Bayesian computing in applications. Students should also understand and be able to discuss the philosophical and practical differences between a Bayesian and classical data analysis and know the strengths and weaknesses of each method.
Topical Outline
Historical introduction Basics of Bayesian analysis--likelihood, prior, posterior Model building, and checking Robustness and sensitivity analysis Comparisons with frequentist approach (theoretical and practical) Computing the posterior distribution Sampling from the posterior distribution MCMC algorithms (Metropolis-Hasting algorithm, Gibbs sampler, modern methods) Hierarchical Bayes modeling Objective Bayesian methods Laplace approximations and asymptotic Bayesian solutions
Syllabus