Approximate Bayesian inference for large-scale epidemic models
Statistical inference for individual-level models of infectious disease spread is often highly 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. For example, generally times of infection and removal of unknown, and very often underlying contact networks through which disease can be transmitted, are also unknown.
Here, we consider the use of approximate methods of inference for such models. Two such methods will be discussed. First, so-called sequential approximate Bayesian computation (s-ABC) methods, in which the likelihood is approximated using a comparison between observed and simulated data. Second, emulation-based methods in which a Gaussian process approximation of the likelihood function built from simulated data is used.
We show evidence that such methods can be used to infer model parameters and underlying characteristics of spatial and network-based disease systems reasonably well, and that this can be done in a computationally efficient manner.