Bayesian statistics, Philosophy and Practice - 2025 entry

Since the 1980s, computational advances and novel algorithms have seen Bayesian methods explode in popularity, today underpinning modern techniques in data analytics, pattern recognition and machine learning as well as numerous inferential procedures used across science, social science and the humanities.

This module will introduce Bayesian statistical inference, describing the differences between it and classical approaches to statistics. It will develop Bayesian methods for data analysis and introduce Bayesian simulation-based techniques for inference. As well as underpinning a philosophical understanding of Bayesian reasoning with theory, we fit a range of models using modern software currently used for Bayesian inference, allowing you to apply techniques discussed in the course to real data.

This module will cover the Bayesian approach to modelling, data analysis and statistical inference. The module describes the underpinning philosophies behind the Bayesian approach, looking at subjective probability theory, the notion and handling of prior knowledge, and posterior inference. We then explore simulation-based inference in Bayesian analyses and develop important algorithms for Bayesian simulation by Markov Chain Monte Carlo (MCMC) such as the Gibbs sampler and the Metropolis-Hastings algorithm. Finally, we’ll use the techniques developed through the module to perform parameter estimation for a range of simple and then more complex hierarchical models.

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

1. Show understanding of the subjective approach to probabilistic reasoning;

2. Demonstrate an awareness of Bayesian approaches to statistical modelling and inference and an ability to apply them in practice;

3. Demonstrate understanding of the value of simulation-based inference and knowledge of techniques such as MCMC and the theories underpinning them;

4. Demonstrate the ability to fit a range of models in the Bayesian framework;

5. Utilise appropriate software and a suitable computer language for Bayesian modelling and inference from data.

6. Demonstrate understanding, appreciation of and aptitude in the quantification of uncertainty using advanced mathematical modelling;

7. Show advanced Bayesian data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;

8. Apply relevant computer software competently;

9. Use learning resources appropriately;

10. Exemplify self-management and time-management skills.

Introduction: Bayesian vs Classical statistics, Nature of probability and uncertainty.

Bayesian inference: Bayes Theorem, Conjugate priors, Objective priors, Subjective priors, Prior and Posterior predictive distributions, Prior elicitation, Posterior summaries and simulation.

Bayesian Computation: Monte Carlo, Inverse CDF, Rejection Sampling, Markov Chain Monte Carlo (MCMC), Gibbs sampling, Metropolis Hastings, Hamiltonian Monte Carlo, Diagnostics.

Modelling: Conjugate models, measurement models, Bayesian regression, Bayesian Hierarchical models, Generalised Linear Models.

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%. 

Basic reading:

• ELE

Web based and Electronic Resources:

Other Resources:

• Lindley, D. V. “Making Decisions”

• De Groot, M. H. “Optimal Statistical Decisions”.

• Sivia, D. S. “Data Analysis, A Bayesian Tutorial”.

Reading list for this module: