Continuous time modelling of dynamical spatial lattice data observed at sparsely distributed times

Summary. We consider statistical and computational aspects of simulation-based Bayesian inference for a spatial-temporal model based on a multivariate point process which is only observed at sparsely distributed times. The point processes are indexed by the sites of a spatial lattice, and they exhibit spatial interaction. For specificity we consider a particular dynamical spatial lattice data set which has previously been analysed by a discrete time model involving unknown normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared with discrete time processes in the setting of the present paper as well as other spatial-temporal situations.