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.

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