Variational approach for spatial point process intensity estimation

Abstract

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the d-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a simple and general setting when the intensity function is assumed to be of log-linear form Β + θT z(u) where z is a spatial covariate function and the focus is on estimating θ. The variational estimator is very simple to implement and quicker than alternative estimation procedures. We establish its strong consistency and asymptotic normality. We also discuss its finite-sample properties in comparison with the maximum first order composite likelihood estimator when considering various inhomogeneous spatial point process models and dimensions as well as settings were z is completely or only partially known. © 2014 ISI/BS.