Extremely contagious, acute, immunizing childhood infections like measles can
exhibit spatiotemporal dynamics that depend on the nature of spatial contagion
and spatiotemporal variations in population structure and demography. We study
a metapopulation model for regional measles dynamics that uses a gravity
coupling model and a time series susceptible- infected-recovered (TSIR) model
for local dynamics. Standard maximum likelihood or Bayesian inference for this
model is infeasible as there are potentially tens of thousands of latent
variables in the model and each evaluation of the likelihood is expensive. We
develop an efficient discretized MCMC algorithm for Bayesian inference with
these expensive likelihood evaluations. However, we find through a simulation
study that parameter estimates are biased and simulations at the obtained
parameter settings do not explain some important biological characteristics of
the data. We propose fitting a Gaussian process (GP) model to forward
simulations of the gravity model at a number of parameter settings. Based on
the GP-based emulator we perform a full Bayesian analysis of a given data set.
This approach allows us to conveniently study posterior distributions of the
key parameters of the gravity model and has number of advantages over the
classic likelihood based inference.