Partial likelihood analysis of spatio-temporal point process data

We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio-temporal point-process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum-likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial-likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain.