Bayesian computing and sampling design for partially-surveyed spatial point process models

Abstract

Spatial point processes model situations such as unexploded ordnance, plant and animal populations, and celestial bodies, where events occur at distinct points in space. Point process models describe the number and distribution of these events. These models have been mathematically understood for many decades, but have not been widely used because of computational challenges. Computing advances in the last 30 years have kept interest alive, with several breakthroughs circa 2010 that have made Bayesian spatial point process models practical for many applications. There is now interest in sampling, where the process is only observed in part of the study site. My dissertation work deals with sampling along paths, a standard feature of unexploded ordnance remediation studies. In this dissertation, I introduce a data augmentation procedure to adapt a Dirichlet process mixture model to sampling situations and I provide the first comparison of a variety of sampling designs with regard to their spatial prediction performance for spatial log-Gaussian Cox process (LGCP) models. The Dirichlet process model remains computationally expensive in the sampling case while the LGCP performs well with low computing time. The sampling design study shows that paths with regular spacing perform well, with corners and direction changes being helpful when the path is short.