- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Pre-requisites for Natural Sciences students: must have taken Statistics Option MAT00033I.
Occurrence | Teaching period |
---|---|
A | Autumn Term 2022-23 |
To introduce the basic notions of Bayesian statistics, showing how Bayes Theorem provides a natural way of combining prior information with experimental data to arrive at a posterior probability distribution over parameters.
To illustrate the differences between classical (sampling theory) statistics and Bayesian statistics.
At the end of the module you should be able to:
Understand the basic notions of Bayesian statistics;
Prove and use Bayes Theorem in its various forms;
Carry out an analysis of normally distributed data with a normal prior distribution;
Carry out analyses of data from Binomial, Poisson and Exponential distributions using conjugate priors;
Perform a Bayesian analysis of data following simple hierarchical models.
Syllabus
Introduction, review of Probability Theory, Bayes Theorem, Exchangeability
Binomial model: prior, likelihood and posterior; predictive distributions
Point estimation, Credibility regions
Poisson model, Poisson model with exposure, Exponential model
Normal model: unknown mean, unknown variance, both mean and variance unknown
Monte Carlo approximation, full conditional distributions, Gibbs sampling
Exponential families and conjugate priors, weakly informative priors, Jeffreys' principle
Hierarchical Models
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Hoff, P.D. (2009). A First Couse in Bayesian Statistical Methods, Springer
Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2004). Bayesian Data Analysis, Second Edition, Chapman & Hall/CRC
Lee, P.M. (2012). Bayesian Statistics: An Introduction, Fourth Edition, Wiley