This chapter contains sections titled: Probability Random Variables, Parameters and Likelihood The Normal Distribution Normal Likelihoods Classical Inference A Catalogue of Useful Distributions* Key Points Exercises

This is the third of four articles Bayes's theorem arose from a posthumous publication in 1763 by Thomas Bayes, a non-conformist minister from Tunbridge Wells. Although it gives a simple and uncontroversial result in probability theory, specific uses of the theorem have been the subject of considerable controversy for more than two centuries. In recent years a more balanced and pragmatic perspective has emerged, and in this paper we review current thinking on the value of the Bayesian approach to health technology assessment. A concise definition of bayesian methods in health technology assessment has not been established, but we suggest the following: the explicit quantitative use of external evidence in the design, monitoring, analysis, interpretation, and reporting of a health technology assessment. This approach acknowledges that judgments about the benefits of a new technology will rarely be based solely on the results of a single study but should synthesise evidence from multiple sources—for example, pilot studies, trials of similar interventions, and even subjective judgments about the generalisability of the study's results. A bayesian perspective leads to an approach to clinical trials that is claimed to be more flexible and ethical than traditional methods,1 and to elegant ways of handling multiple substudies—for example, when simultaneously estimating the effects of a treatment on many subgroups.2 Proponents have also argued that a bayesian approach allows conclusions to be provided in a form that is most suitable for decisions specific to patients and decisions affecting public policy.3 #### Summary points Bayesian methods interpret data from a study in the light of external evidence and judgment, and the form in which conclusions are drawn contributes naturally to decision making Prior plausibility of hypotheses is taken into account, just as when interpreting the results of a diagnostic test Scepticism about large treatment effects can be formally …