Statistics 4870/6870: Description

Bayes Theorem, subjective probability, conjugate priors, non-informative priors, posterior estimation, credible intervals, prediction, sensitivity analysis, comparison to classical procedures, MCMC, Gibbs sampling, hierarchical Bayesian analysis. Use of statistical software. Report writing. Prerequisites: a graduate level course in Statistics or probability and an upper division course in computational statistics or computer science or consent of instructor. Co-requisite: one of prerequisites allowed as co-requisite.

In this course will will introduce the Bayesian approach to Statistical Inference. 

• Bayes' Theorem will be reviewed. 
• The concept of a prior distribution will be introduced.
• Posterior distribution calculations via proportional calculations from the likelihood and prior distribution.
• MCMC methods will be presented (Gibbs Sampling).
• WinBUGS will be used along with some R programs to implement the methods.
• Topics will be covered from many standard and non-standard statistical problems from a Bayesian perspective.