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Description
This module aims to introduce the Bayesian approach to statistical inference, to develop relevant theory, methodology and computational techniques for its implementation and to develop basic skills in the use of probabilistic programming software for Bayesian modelling. It is primarily intended for students registered on the Masters degree programmes offered by the Department of Statistical Science (including the CSML, DSML and MASS programmes).听For these students, the academic prerequisites for this module are met either through earlier compulsory study within (UG) or successful admission to (PGT) their current programme.
Intended Learning Outcomes
- be able to give an account of the underlying principles of Bayesian inference and the use of prior information;
- be able to听manipulate probability formulae to derive posterior and predictive distributions;
- be able to perform conjugate prior-to-posterior analysis for simple binomial, Poisson and normal models;
- be able to compare simple models using Bayes factor and to understand how these methods can be extended to more complex models;
- be able to use听hierarchical, latent variable and graphical modelling to represent and analyse complex systems;
- be able to demonstrate critical understanding of the use of sampling-based and optimisation-based methods for Bayesian inference;
- be able to use probabilistic programming to fit complex Bayesian models.
Applications - Bayesian methods are currently gaining increasing popularity, largely because advances in computing facilities and in modern simulation-based Markov Chain Monte Carlo (MCMC) methods provide a means of analysing the complex data structures that arise in application areas as diverse as artificial intelligence, biology, genetics and environmental science. This module focuses on fundamental concepts and techniques, and introduces the computational tools needed to apply Bayesian methods in challenging research-level problems.
Indicative Content - Introduction to Bayesian statistics. Bayesian inference. Prior distributions. Graphical models. Hierarchical models. Markov chain Monte Carlo (MCMC: Gibbs sampling). Probabilistic programming software.
Key Texts - Available from .
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 8th April 2024.
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