Rob Deardon, PhD

Statistical inference for spatial models of infectious disease spread is often very computationally expensive. Such models are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework, which requires multiple calculation of what is often a computationally cumbersome likelihood function. This problem is especially severe when there are large numbers of latent variables to compute. Here, we propose two methods of inference based on so-called emulation techniques. One method consists of approximating the likelihood via a Gaussian process built using “ABC-style” summary statistics. The second method consists of approximating the likelihood directly with the Gaussian process, but using pseudo-marginal approximations to allow for latent variables such as infectious periods. These methods are set in a Bayesian MCMC context, but avoid calculation of the computationally expensive likelihood function by replacing it via the aforementioned Gaussian processes. We show that such methods can be used to infer the model parameters and underlying characteristics of spatial disease systems, and that this can be done in much more computationally efficient manner than full Bayesian MCMC allows.