A0761
Title: Semi-parametric inference for doubly stochastic spatial point processes
Authors: Ali Shojaie - University of Washington (United States) [presenting]
Abstract: Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantees, and/or rely on restrictive assumptions. A penalized regression method is presented for estimating covariate effects in doubly-stochastic point processes that are computationally efficient and do not require a parametric form or stationarity of the underlying intensity. The approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. It is shown that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit conservative, statistical inference procedure. Simulation studies show the validity of our approach under less restrictive assumptions on the data-generating mechanism and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.
