Master of Mathematics (MMath)

MMath Mathematics

  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: G104 / Institution code: M20
  • Key features:
  • Scholarships available
  • Accredited course

Full entry requirementsHow to apply

Course unit details:
Bayesian Statistics

Course unit fact file
Unit code MATH48221
Credit rating 15
Unit level Level 4
Teaching period(s) Semester 1
Available as a free choice unit? No

Overview

The unit aims to introduce students to the fundamentals of Bayesian inference and the computational techniques used to apply it in data analysis and model evaluation. 

Pre/co-requisites

Unit title Unit code Requirement type Description
Probability and Statistics 2 MATH27720 Pre-Requisite Compulsory

Aims

The unit aims to:  

Introduce students to the fundamentals of Bayesian inference and the computational techniques used to apply it in data analysis and model evaluation. 

Learning outcomes

On the successful completion of the course, students will be able to:

  1. Derive posterior distributions for exact Bayesian inference and make inferences/predictions based on these posteriors;
  2. Apply various computational algorithms to obtain samples from complex posterior distributions and for parameter estimation;
  3. Describe the various algorithms in words but also implement key algorithms through statistical software;
  4. Make informed choices among available algorithms for practical data analysis;
  5. Solve statistical modelling and inference problems within the Bayesian paradigm.

Syllabus

Part A – Foundation of Bayesian Inference

  • Bayesian inference concepts: single and multiple parameter prior and posterior distributions; conjugacy and non-conjugacy; Bayesian estimators; credible intervals.
  • Model checking & model comparison: Posterior predictive distribution; Bayesian forecasting; model comparison based on predictive performance; model comparison criteria such as Bayes factors, BIC and DIC; Bayesian Decision Theory; Laplace's approximation.

Part B - Computational Bayesian Statistics

  • Gibbs Sampler: data augmentation; burn-in; convergence.
  • Metropolis-Hasting’s algorithm: independent sampler; random walk Metropolis; scaling; multi-modality.  
  • MCMC Issues: Monte Carlo Error (batch means/window estimates for MCSE); reparameterization; hybrid algorithms; convergence diagnostics for single/multiple chains.  
  • Hamiltonian Monte Carlo.
  • Approximate Bayesian Inference.

Teaching and learning methods

Teaching is composed of two hours of lectures and one example/computer class per week. Teaching materials will be made available online for reference and review. 

Assessment methods

Method Weight
Other 30%
Written exam 70%

Coursework: 1 x CW assignment on computational aspects of Bayesian statistics - weighted 30%

Exam: 3 hours - weighted 70%

Recommended reading

Christensen, R., Johnson, W., Branscum, A., & Hanson, T. E. (2010). Bayesian ideas and data analysis: an introduction for scientists and statisticians. CRC press.

 

Heard, N. (2021). An introduction to Bayesian inference, methods and computation. Cham: Springer.

 

McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and Stan, (2nd edn). Chapman and Hall/CRC.

 

Wang, X., Yue, Y. R., & Faraway, J. J. (2018). Bayesian regression modeling with INLA. Chapman and Hall/CRC. 

Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 117

Teaching staff

Staff member Role
Taban Baghfalaki Unit coordinator

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