Dr Konstantinos Kalogeropoulos COL.610

This course is available on the BSc in Actuarial Science, BSc in Data Science, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. 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 one of the following two combinations of courses: (a) ST102 and MA100, or (b) MA107 and ST109 and EC1C1. Equivalent combinations may be accepted at the lecturer’s discretion. ST202 is also recommended.

Previous programming experience is not required  but students who have no previous experience in R must complete an online pre-sessional R course from the Digital Skills Lab before the start of the course (https://moodle.lse.ac.uk/course/view.php?id=7745)

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, Monte Carlo methods), Markov Chain Monte Carlo (MCMC) simulation (Gibbs sampler, Metropolis-Hastings algorithm). Computer tools (R).

Applications: Linear models in Regression and Classification (Bayesian Linear Regression, Generalized Linear Models, Logistic Regression), Hierarchical/ Multilevel Models, Bayesian Nonparametrics.

This course will be delivered through a combination of classes, lectures, and Q&A sessions, totalling a minimum of 29 hours across the Winter Term. 

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 spring exam period.
Project (20%) in the ST.