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:

• understand the fundamentals of Bayesian inference, and how it differs from frequentist inference;
• appreciate the role of the prior distribution, how it may be constructed, and its basis in the personal interpretation of probability;
• have intuitive understanding of how Bayes’ theorem synthesises prior information and data;
• be able to derive the posterior distribution and appropriate summaries/inferences in simple situations;
• be aware of how more complex problems are tackled, through hierarchical modelling and modern computational tools;
• understand the benefits of Bayesian analysis, the extra demands that it makes, and the kinds of problems where it is proving to be most powerful.

Synopsis

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.