Co-requisite: MA881: Probability and Classical Inference
OverviewBayes Theorem for density functions; Conjugate models; Predictive distribution; Bayes estimates; Sampling density functions; Gibbs and Metropolis-Hastings samplers; Winbugs/OpenBUGS; Bayesian hierarchical models; Bayesian model choice; Objective priors; Exchangeability; Choice of priors; Applications of hierarchical models.
This module appears in:
Method of assessment
80% examination and 20% coursework
A.F.M. Smith and Bernardo, J.M. (1994). Bayesian Theory. Wiley.
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 demonstrate systematic understanding of key aspects of Bayesian Statistics;
2 demonstrate the capability to solve complex problems using a very good level of skill in calculation and manipulation of the material in the following areas: derivation of posterior distributions; computation of posterior summaries, including the predictive distribution; construction of Bayesian hierarchical models and their estimation using Markov chain Monte Carlo methods; critical evaluation and interpretation of software output.
3 apply a range of concepts and principles in Bayesian Statistics in loosely defined contexts, showing good judgement in the selection and application of tools and techniques;
4 show judgement in the selection and application of R and WinBugs/OpenBugs.
The intended generic learning outcomes. On successfully completing the module students will be able to:
1 manage their own learning and make use of appropriate resources.
2 understand logical arguments, identifying the assumptions made and the conclusions drawn
3 communicate straightforward arguments and conclusions reasonably accurately and clearly
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working
5 solve problems relating to qualitative and quantitative information
6 make competent use of information technology skills such as R and WinBugs/OpenBugs, online resources (Moodle), internet communication.
7 communicate technical material competently
8 demonstrate an increased level of skill in numeracy and computation