This chapter describes how Markov chain Monte Carlo methods can be used to analyze data from outbreaks of infectious disease. Specifically, methods are described for Bayesian estimation of the parameters of stochastic disease transmission models. The methods are highly flexible in nature, being applicable to a wide range of models and types of data. The methods also can cater for missing data, particularly in the sense that the actual process of infection need not be observed, as is typical in practice.

As well as providing details of the Markov chain Monte Carlo methods, practical guidelines are given in the chapter. The methods are illustrated in detail for a simple example featuring a simple susceptible-infective-removed model, and also a more complex example of a real-life data set on a measles outbreak.