Prospectus

# Bayesian Statistics

Course 2015-2016

Basic statistics and a good notion of regression models.

## Description

We introduce the Bayesian philosophy and terminology and contrast it with the frequentist approach from both a methodological as well as a historical perspective. The Bayesian interpretation and use of probability is discussed. Subjective, conjugate and non-informative prior distributions for model specification are investigated. Bayesian concepts like posterior mean, median, credible interval are introduced and illustrated. Modern Bayesian Data analysis requires highly sophisticated and very computer intensive methods. The course provides a review of the most important numerical techniques, which are useful to calibrate Bayes models. Two Markov Chain Monte Carlo (MCMC) techniques: Gibbs and Metropolis-Hastings sampling with its adaptive variants will be covered in detail. The background of these approaches will be explained and exemplified using a variety of examples. Students are taught how to apply these methods with modern Bayesian software to model complex data. 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. The background and applicability of integrated nested Laplace approximation (INLA) for these models is highlighted. We discuss the Bayesian approach to account for model uncertainty, discuss Bayesian variable selection and Bayesian model adaptation to high-dimensional statistics applications. Concepts of latent variable modelling and data augmentation to simplify model specification and computation is reviewed. Application and use of the Bayes formalism for predictive inference is discussed, together with posterior predictive model checking for the critical assessment of models. A variety of medical, epidemiological and clinical trials studies will be used for illustrative purposes.

## Course objectives

After the course you can tell about the key issues in Bayesian data analysis and are able to set up and analyze some basic Bayesian models.

## Mode of Instruction

This course is a combination of lectures, problem sessions and computer practicals using FirstBayes, R, and WinBugs/OpenBugs.

## Time Table

For the course days, course location and class hours check the Time Table under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience

## Assessment method

Written exam (2/3) and assignments (1/3)

Date information about the exam and resit can be found in the Time Table pdf document under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience. The exams take place in the Snellius building, the room will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed online at:“http://info.liacs.nl/math/”:http://info.liacs.nl/math/
If the exam does not take place in the Snellius building, then an announcement will be sent via blackboard.

Compulsory:

• Lesaffre, E. & Lawson, A. B. Bayesian Biostatistics. Statistics in Practice.Wiley, New York, 2012.
Optional:
• Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, Chapman & Hall (2nd edition), 2003 Press, S.J. Subjective and Objective Bayesian Statistics: Principles, Models and Applications, John Wiley & Sons, New York, 2003.
• Spiegelhalter, D.J., Abrams, K.R. and Myles, J.P. Bayesian Approaches to Clinical Trials and HealthCare Evaluation, John Wiley & Sons, New York, 2004.

## Registration

Enroll in Blackboard for the course materials and course updates.

To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

## Contact information

cajo [dot] terbraak [at] wur [dot] nl

## Remarks

• This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.