# Bayesian Statistics (MS)

Course
2011-2012

The aims are to introduce the Bayesian philosophy and terminology and to contrast it with the frequentist approach. It provides a review of the most important numerical techniques, which are useful to arrive at a Bayesian solution. Also, students are taught how to use Bayesian software to model complex data.
The Bayesian approach is introduced and contrasted to the frequentist approach both from an historical perspective as from a methodological viewpoint and this will be done at various instances in the course. Bayesian concepts like posterior mean, median, credible interval are introduced and illustrated using e.g. 1stBayes. The Bayesian interpretation of probability is treated, including subjective (enthusiastic, sceptical), conjugate and non-informative prior distributions. Modern Bayesian Data analysis requires highly sophisticated and very computer intensive methods. Two Markov Chain Monte Carlo (MCMC) techniques: Gibbs and Metropolis-Hastings sampling will be covered. The background of these approaches will be explained and exemplified using a variety of examples. Convergence diagnostics and convergence acceleration are important for the practical feasibility of the MCMC approaches and they will be treated in detail. The important class of hierarchical models (including repeated measurements studies, multi-level models, cluster-randomized trials, etc.) will be reviewed in a Bayesian context. A variety of medical, epidemiological and clinical trials studies will be used for illustrative purposes.

The course consists of lectures and graded homework assignments.

Prerequisites
Basic statistics and a good notion of regression models

Performance objectives
Performing a comprehensive Bayesian analysis for (rather) complex data structures.

Examination
Project in groups with individual oral defence

Literature (compulsory)
Course notes “Bayesian Statistics” Lesaffre E. and Lawson A. (2010) Bayesian Biostatistics (in preparation), Wiley

Literature (optional) – Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2003). Bayesian Data Analysis (2nd edition). Chapman & Hall – Press, S.J. (2003). Subjective and Objective Bayesian Statistics: Principles, Models and Applications. John Wiley & Sons, New York. – Spiegelhalter, D.J., Abrams, K.R. and Myles, J.P. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation, John Wiley & Sons, New York.

Software
FirstBayes, R, WinBugs and SAS