Bayesian Inference

Description

STAT314 and STAT461 introduce theory and application of Bayesian Inference. Due to recent advances in computing and to the existence of some relatively user-friendly software Bayesian methods are becoming more and more popular in many applied fields of study, including epidemiology, bioinformatics, ecology and archaeology. This course will cover the basics of Bayesian theory as well as introduce computing methods necessary for implementation of this theory in practice. In addition to generalised linear regression models, analysis of variance and basic tests, for which the results of Bayesian inference will be compared with those for the classical frequentist results, the course will demonstrate the attractive flexibility and multifacetedness of Bayesian methods considering such problems as threshold analysis, and Poisson change-point problems among others.

Topics that are usually covered include:
• Bayes’ Inverse Probability Formula and Bayes’ Theorem. The concepts of prior and posterior distributions. Posterior predictive distribution. Various types of prior distributions.
• Bayesian model comparison and Bayesian model averaging.
• Numerical tools for Bayesian estimation: Markov Chain Monte Carlo (MCMC) methods, Gibbs sampler and Metropolis-Hasting sampler.
• Bayesian inference on linear regression models, generalised linear models, and mixed-effects models.
• Treatment of missing data and latent parameters

The statistical computations will be performed using a combination of WinBUGS (a software for Bayesian inference) and R (a statistical software package). Prior knowledge of WinBUGS is not required. Prior knowledge of R is desirable.