Estimating likelihoods for spatio-temporal models using importance sampling

This paper describes how importance sampling can be applied to estimate likelihoods for spatio-temporal stochastic models of epidemics in plant populations, where observations consist of the set of diseased individuals at two or more distinct times. Likelihood computation is problematic because of the inherent lack of independence of the status of individuals in the population whenever disease transmission is distance-dependent. The methods of this paper overcome this by partitioning the population into a number of sectors and then attempting to take account of this dependence within each sector, while neglecting that between-sectors. Application to both simulated and real epidemic data sets show that the techniques perform well in comparison with existing approaches. Moreover, the results confirm the validity of likelihood estimates obtained elsewhere using Markov chain Monte Carlo methods.