Bayesian inference for stochastic multitype epidemics in structured populations using sample data.

This paper is concerned with the development of new methods for Bayesian statistical inference for structured-population stochastic epidemic models, given data in the form of a sample from a population with known structure. Specifically, the data are assumed to consist of final outcome information, so that it is known whether or not each individual in the sample ever became a clinical case during the epidemic outbreak. The objective is to make inference for the infection rate parameters in the underlying model of disease transmission. The principal challenge is that the required likelihood of the data is intractable in all but the simplest cases. Demiris and O'Neill (2005b) used data augmentation methods involving a certain random graph in a Markov chain Monte Carlo setting to address this situation in the special case where the sample is the same as the entire population. Here, we take an approach relying on broadly similar principles, but for which the implementation details are markedly different. Specifically, to cover the general case of sample data, we use an alternative data augmentation scheme and employ noncentering methods. The methods are illustrated using data from an influenza outbreak.