Simulation-based Bayesian inference for epidemic models

A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods.