Title: Scalable Inference for Space-Time Gaussian Cox Processes,
Abstract: The log-Gaussian Cox process is a flexible and popular class of point pattern
models for capturing spatial and space-time dependence for point patterns.
Model fitting requires approximation of stochastic integrals which is
implemented through discretization over the domain of interest. With fine scale
discretization, inference based on Markov chain Monte Carlo is computationally
burdensome because of the cost of matrix decompositions and storage, such as
the Cholesky, for high dimensional covariance matrices associated with latent
Gaussian variables. This article addresses these computational bottlenecks by
combining two recent developments: (i) a data augmentation strategy that has
been proposed for space-time Gaussian Cox processes that is based on exact
Bayesian inference and does not require fine grid approximations for infinite
dimensional integrals, and (ii) a recently developed family of
sparsity-inducing Gaussian processes, called nearest-neighbor Gaussian
processes, to avoid expensive matrix computations. Our inference is delivered
within the fully model-based Bayesian paradigm and does not sacrifice the
richness of traditional log-Gaussian Cox processes. We apply our method to
crime event data in San Francisco and investigate the recovery of the intensity
surface.