Dr Konstantinos Kalogeropoulos COL.610

This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

Students must have completed Mathematical Methods (MA100) and Elementary Statistical Theory (ST102).

ST202 is also recommended.

Statistical decision theory: risk, decision rules, loss and utility functions, Bayesian expected loss, Frequentist risk.

Bayesian Inference: Bayes theorem, prior, posterior and predictive distributions, conjugate models (Normal-Normal, Poisson-Gamma, Beta-Binomial), Bayesian point estimation, credible intervals and hypothesis testing, Bayes factors and model selection. Comparison with Frequentist approaches.

Implementation: Asymptotic approximations (Laplace approximation, Variational Bayes, Monte Carlo methods), Markov Chain Monte Carlo (MCMC) simulation (Gibbs sampler, Metropolis-Hastings algorithm). Computer tools (R, Stan).

Applications: Linear models in Regression and Classification (Bayesian Linear Regression, Generalized Linear Models, Logistic Regression), Cluster Analysis and Mixture Modeling, Hierarchical/ Multilevel Models.

20 hours of lectures and 9 hours of computer workshops in the LT. 2 hours of lectures in the ST.

There will be no reading week in week 6, but there will be no lectures and classes in week 11.

Optional problem sets and computer exercises.

J.K. Kruschke, Doing Bayesian Data Analysis. An tutorial with R, JAGS and Stan. 2nd edition.

J.O. Berger, Statistical Decision Theory and Bayesian Analysis.

D. Gamerman, H. F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference

A. Gelman, Bayesian data analysis.

Exam (80%, duration: 2 hours) in the summer exam period.
Project (20%) in the ST.