Bayesian inference is a set of methods where the probability of an event occurring can be updated as more information becomes available. It is fundamentally different from frequentist methods, which are based on long running relative frequencies. This module gives an introduction to the Bayesian approach to statistical analysis and the theory that underpins it.
Students will be able to explain the distinctive features of Bayesian methodology, understand and appreciate the role of prior distributions and compute posterior distributions. It will cover the derivation of posterior distributions, the construction of prior distributions, and inference for missing data. Extensions are considered to models with more than a single parameter and how these can be used to analyse data. Computational methods have greatly advanced the use of Bayesian methods and this module covers, and allows students to apply, procedures for the sampling and analysis of intractable Bayesian problems.
Learning Outcomes
By the end of this module, students should be able to: Demonstrate a full and rigorous understanding of all definitions associated with Bayesian inference and understand the differences between the Bayesian and frequentist approaches to inference
Demonstrate a sound understanding of the fundamental concepts of Bayesian inference and computational sampling methodsUnderstand how to make inferences assuming various population distributions while taking into account expert opinion and the implications of weak prior knowledge and large samples
Demonstrate an understanding of the principles of Markov Chain Monte Carlo and be able to programme an MCMC algorithmEngage in Bayesian data analysis in diverse situations drawn from physics, biological, engineering and other mathematical contexts.
Assessment
39658-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
Assessment:
50% Continuous Assessment (based on a combination of project work, Class Tests and/or Problem Sheets, as specified by the Lecturer). 50% Final Examination, 1hr 30m written unseen.
Reassessment: 1.5 hour resit examination (50%) during supplementary examination period and project task (50%) completed over summer. Resit Capped at pass threshold (50%).
