University of Sheffield

Tony O'Hagan - Academic pages


Short course: Introduction to Bayesian Statistics

This two-day course provides a basic grounding in the theory and concepts of Bayesian inference. Whilst many participants will have encountered the Bayesian approach to some extent, no specific background knowledge is assumed.

Learning Objectives

At the end of the course, participants should:


The course is structured as 8 lectures plus 3 exercise/practical sessions. Lecture topics are as follows.
  1. The Bayesian paradigm. Bayes’ theorem, prior, likelihood and posterior. Simple one-parameter models.
  2. Some standard models. A detailed analysis of the cases of binomial and normal samples.
  3. Inference. Bayesian inferences, and how they differ from frequentist inferences. Formal and informal inference.
  4. Prior. Personal probability. Elicitation. ‘Default’ prior distributions. Interpretation of inferences.
  5. Bayes theory. Likelihood, sufficiency and ancillarity. Asymptotics. Preposterior analysis.
  6. Structuring prior information. Independence and exchangeability. Hierarchical models. Shrinkage and smoothing.
  7. Tackling real problems. Bayesian modelling and computation. Outline of a real example to show how Bayesian analysis works in complex problems.
  8. For and against. What do we get from a Bayesian analysis, and at what cost? In what situations does the Bayesian approach give the greatest benefit?

The first practical/tutorial session is a practical exercise in specifying beliefs about exchangeable sequences. The second provides experience with theoretical manipulations. The third involves a role-play exercise and group work.

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Updated: 13 January 2017
Maintained by: Tony O'Hagan