Doubly stochastic models for replicated spatio-temporal point processes

Abstract: This paper proposes a log-linear model for the latent intensity functions of a replicated spatio-temporal point process. By simultaneously fitting correlated spatial and temporal Karhunen-Lo`eve expansions, the model produces spatial and temporal components that are usually easy to interpret and capture the most important modes of variation and spatio-temporal correlation of the process. The asymptotic distribution of the estimators is derived. The finite sample properties are studied by simulations. As an example of application, we analyze bike usage patterns on the Divvy bike sharing system of the city of Chicago.