Collapsing of Non‐centred Parameterized MCMC Algorithms with Applications to Epidemic Models

Data augmentation is required for the implementation of many Markov chain Monte Carlo (MCMC) algorithms. The inclusion of augmented data can often lead to conditional distributions from well‐known probability distributions for some of the parameters in the model. In such cases, collapsing (integrating out parameters) has been shown to improve the performance of MCMC algorithms. We show how integrating out the infection rate parameter in epidemic models leads to efficient MCMC algorithms for two very different epidemic scenarios, final outcome data from a multitype SIR epidemic and longitudinal data from a spatial SI epidemic. The resulting MCMC algorithms give fresh insight into real‐life epidemic data sets.