Spatiotemporal prediction for log-Gaussian Cox processes

Abstract

Space-time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space-time point processes. Our models are Cox processes whose stochastic intensity is a space-time Ornstein-Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.