Thinning spatial point processes into Poisson processes

Abstract This paper describes methods for randomly thinning two main classes of spatial point processes, viz. Markov point processes and Cox processes. The procedure, which relies on a fitted modelλ for either the Papangelou conditional intensity for a Markov point process or the random intensity function for a Cox process, results in a Poisson process if and only if the true λ is used, and thus can be used as a diagnostic for assessing the goodness-of-fit of a spatial point process model. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-anddeath process, where clans of ancestors associated with the original points are identified, and where one simulates backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is used. The utility of the proposed methods is limited to cases where λ is bounded from below by a strictly positive function. Several examples, including clustered and inhibitive point processes, are considered