This course is intended for doctoral and PhD students who want to gain a deeper understanding of Bayesian Computing. The following topics will be covered:

• Introductory Bayesian computations (computing integrals, Monte Carlo methods, importance sampling)
  
• Markov chain Monte Carlo methods (Metropolis-Hastings algorithm, Gibbs sampling, MCMC output analysis)
  
• The principle of data augmentation (Gibbs sampling based on data augmention, simple methods for boosting MCMC)
• Hierarchical models (random effects moels, mixture models, Bayesian regularization)
• Bayesian model comparison and model selection (Bayes factors, marginal likelihoods, variable selection in a regression model, priors for model selection)
  

After completing this course the student will have the ability to:

• Recall the basic principle of Bayesian inference (prior distribution, posterior distribution, predictive distribution, model evidence)
• Recall the basic principle of Bayesian computing based on Monte Carlo simulation methods
• Apply public domain packages for Bayesian inference and to analyse and evaluate the output of such packages
• Design and implement computer programs for solving computational problems in Bayesian inference for commonly applied statistical models
  

This course is taught as lectures combined with assigments which have to be solved individually by the students. In addition, a course project is developped in groups and students make a presentation at the end of the term.

In combination with the lecture, the assignments and the course project will help students to consolidate and expand their understanding of the theoretical and applied methods discussed in the lectures.

Grading is based on 4 assignment which have to be solved and submitted  individually by each student and a projects which is developped in groups of two or three students and has to be presented  at the end of the course. The assessment will be based on the correctness of results, the clarity of the presentation, the ability to describe and apply the key concepts discussed throughout the course, and the recognizable effort made.

Each assignement accounts for 15% of the final grade, whereas the final presentation accounts for 40% of the grade.

Final grading is as follows: 1 (at least 90%),  2 (at least 80%),  3 (at least 70%), 4 (at least 60%),5 (less than 60%).