Prerequisite module: MAST5007 Mathematical Statistics
OverviewThe origins of Bayesian inference lie in Bayes' Theorem for density functions; the likelihood function and the prior distribution combine to provide a posterior distribution which reflects beliefs about an unknown parameter based on the data and prior beliefs. Statistical inference is determined solely by the posterior distribution. So, for example, an estimate of the parameter could be the mean value of the posterior distribution. This module will provide a full description of Bayesian analysis and cover popular models, such as the normal distribution. Initially, the flavour will be one of describing the Bayesian counterparts to well known classical procedures such as hypothesis testing and confidence intervals. Outline Syllabus includes: Bayes Theorem for density functions; Exchangeability; Choice of priors; Conjugate models; Predictive distribution; Bayes estimates; Sampling density functions; Gibbs samplers; OpenBUGS; Bayesian hierarchical models; Applications of hierarchical models; Bayesian model choice.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari and D.B. Rubin (2014). Bayesian Data Analysis. 3rd Edition, Chapman & Hall/CRC Texts in Statistical Science
D. Gamerman and H.F. Lopes (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. 2nd Edition, Taylor and Francis.
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 derive posterior distributions when analytically tractable;
2 derive posterior summaries, such as estimates, from the posterior distribution, including the predictive distribution;
3 construct Bayesian hierarchical models and implement them in a suitable software package;
4 critically evaluate software output using convergence diagnostics;
5 interpret and report the output for inferential purposes.
The intended generic learning outcomes. On successfully completing the module students will be able to:
1 use a logical mathematical approach to solve problems;
2 work with relatively little guidance;
3 solve problems and communicate in writing more effectively.