Bayesian Statistics - MAT00003H

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

Pre-requisites for Natural Sciences students: must have taken Statistics Option MAT00033I.

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

Module aims

  • 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.

Module learning outcomes

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.

Module content

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

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Module feedback

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.

Indicative reading

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