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Bayesian Statistics

Vak 2013-2014

Admission requirements

Basic statistics and a good notion of regression models.

Description

The aims are to introduce the Bayesian philosophy and terminology and to contrast it with the
frequentist approach. The course 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. The Bayesian interpretation of probability is treated, including subjective, conjugate and non-informative prior distributions. Bayesian concepts like posterior mean, median, credible interval are introduced and illustrated using e.g. 1stBayes. Modern Bayesian Data analysis requires highly sophisticated and very computer intensive methods. Two Markov Chain Monte Carlo (MCMC) techniques: Gibbs and Metropolis-Hastings sampling with its adaptive variants 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.

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 2013-14 under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience

Assessment method

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

The weekly assignments are handed in each following Monday before the start of the lecture.

The written exam is scheduled for 28 March 2014 from 10.00h-13.00h. The re-sit is scheduled for June 25, 2014 from 14.00h to 17.00h.

Reading list

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

Besides the registration for the (re-)exam in uSis, course registration via blackboard is compulsory.

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.