Doubly stochastic models for spatio-temporal covariation of replicated point processes

This article proposes log-linear models for the latent intensity functions of replicated spatio-temporal point processes. By simultaneously fitting correlated spatial and temporal Karhunen-Loeve expansions, these models produce spatial and temporal components that are usually easy to interpret and capture the main directions of spatio-temporal correlation. The asymptotic distribution of the estimators is derived, and their finite sample properties are studied by simulation. As an example of application, we analyze the spatio-temporal patterns of usage of a bike station in the Divvy bike-sharing system of the city of Chicago.