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Activity Number: 111 - Application and Development of Statistical Methods for Spatio-Temporal Data
Type: Contributed
Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #323236
Title: Spatio-Temporal Log-Gaussian Cox Point Processes via Flexible Gaussian Random Fields
Author(s): Shuwan Wang* and Athanasios Micheas and Christopher K. Wikle
Companies: University of Missouri-Columbia and University of Missouri-Columbia and University of Missouri
Keywords: Spatial-temporal point pattern; Log-Gaussian Cox Process; Bayesian linear regression; modified Cholesky Decomposition; MCMC

Log-Gaussian Cox processes represent an important class of models for spatial and spatial-temporal point pattern data. In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance follows a specific parametric form. These assumptions are restrictive and are not appropriate in many applications. Given replicate observations of a Gaussian spatial field, we propose a novel and flexible Bayesian inference approach for spatial dependence for such processes. In particular, we decompose the latent Gaussian process spatial covariance via a modified Cholesky decomposition within hierarchical Bayesian framework. This reparameterization allows covariance matrix parameters to be represented with a conditionally linear structure that facilitates posterior computation via the use of normal conjugate priors, and allows for covariates to inform the covariance structure. We demonstrate the methods using simulated data and an application to lighting strike data.

Authors who are presenting talks have a * after their name.

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