# Bayesian Statistics

Course
2021-2022

Basic probability and statistics [e.g. https://studiegids.universiteitleiden.nl/en/courses/97199/statistics-and-probability], a good notion of regression models [e.g. https://studiegids.universiteitleiden.nl/en/courses/96305/linear-generalized-linear-models-and-linear-algebra], and familiarity with R [e.g. https://studiegids.universiteitleiden.nl/en/courses/96257/statistical-computing-with-r].

## Description

We will introduce the Bayesian methodology and point out its differences from the frequentist approach to statistics. We will review methods for specifying prior distributions and summarising the posterior distributions. From a computational point of view, we will cover the most important numerical techniques that are used to calibrate Bayesian models. In particular, two Markov Chain Monte Carlo (MCMC) algorithms, the Gibbs and the Metropolis-Hastings samplers, will receive a thorough treatment. Convergence diagnostics and convergence acceleration are important for feasibility of MCMC techniques in practice and they will be studied in detail. We will discuss applications and the use of the Bayesian formalism in predictive inference, together with posterior predictive model checking. An important class of hierarchical and regression models will be reviewed in the Bayesian context. We will introduce Bayesian approaches to model selection, including high-dimensional statistical applications. A variety of medical, epidemiological and clinical trials studies will be utilised as illustrations. Finally, we will highlight the role of Bayesian techniques in machine learning applications.

## Course objectives

Upon completion of the course, the student can identify and explain the key issues in Bayesian data analysis. She is able to set up and analyse Bayesian models of varying degrees of complexity using modern software (R and WinBugs/OpenBugs).

## Mode of Instruction

This course is a combination of lectures, problem sessions and computer classes.

## Time Table

See the Leiden University students' website for the Statistical Science programme -> Schedules

## Assessment method

Written exam (3/4) and assignments (1/4)

Compulsory:

Lesaffre, E. & Lawson, A. B. Bayesian Biostatistics. John Wiley & Sons, Ltd. ISBN 9780470018231.
Additionally, several handouts will be supplied.

## Registration

Enroll in Usis/Brightspace for the course materials and course updates.

To be able to obtain a grade and the EC 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

Bart Mertens: b[dot]mertens[at]lumc[dot]nl
Shota Gugushvili: shota [dot] gugushvili [at] wur [dot] nl