Bayesian Statistics, Philosophy and Practice - 2019 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 the ideas of subjective probability theory for decision-making and explore the place that subjectivity has in scientific reasoning. It will develop Bayesian methods for data analysis and introduce modern Bayesian simulation-based techniques for inference. As well as underpinning a philosophical understanding of Bayesian reasoning with theory, we will use software currently used for Bayesian inference in the lab allowing you to apply techniques discussed in the course to real data.



Pre-requisite skills/knowledge: An undergraduate course in probability theory covering key ideas such as marginalisation and conditioning, and core probability distributions (Normal, Binomial, Gamma, Exponential, Beta (Exeter MTH1004 and its predecessor are sufficient). Likelihood inference (estimation, confidence intervals) at undergraduate level, including exposure to the linear model - for example Exeter ECM2709, preferably the linear model seen in ECM2710 (though this is not a pre-requisite) .

The module runs parallel with the Level 3 course of the same name (ECM3741), with additional M-level material on advanced Bayesian sampling techniques, and their implementation within Bayes, studied independently and assessed as part of an extended Level 3 coursework assignment.


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, subjectivity in science, as well as the notion and handling of prior knowledge and the theory of decision-making under uncertainty. We then move to Bayesian modelling and inference looking at parameter estimation in simple models and then hierarchical models. Finally, we explore simulation-based inference in Bayesian analyses and develop important algorithms for Bayesian simulation by Markov Chain Monte Carlo (MCMC), such the Gibbs sampler and the Metropolis-Hastings algorithm.

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

Module Specific Skills and Knowledge

Discipline Specific Skills and Knowledge

Personal and Key Transferable / Employment Skills and Knowledge

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

 

Decision Theory: Bayes’ rule, Bayes’ risk, Decision trees, Sequential decision-making, Utility. 



Bayesian inference: Conjugate models, Prior and Posterior predictive distributions, Posterior summaries and simulation, Objective and subjective priors, Bayesian regression, Hierarchical models. 



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

M level only, advanced MCMC techniques (for example, from Sliced Sampler; Adaptive Metropolis)


Basic reading:

ELE: http://vle.exeter.ac.uk/

 

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: