Bayesian Analysis of Spatial Point Patterns

• Main Author: Leininger, Thomas Jeffrey
• Other Authors: Gelfand, Alan E
• Published: 2014
• Subjects: Statistics; cross-validation; Gibbs process; Log-Gaussian Cox process; model selection; point pattern residuals; Poisson process
• Online Access: http://hdl.handle.net/10161/8730

<p>We explore the posterior inference available for Bayesian spatial point process models. In the literature, discussion of such models is usually focused on model fitting and rejecting complete spatial randomness, with model diagnostics and posterior inference often left as an afterthought. Posterior predictive point patterns are shown to be useful in performing model diagnostics and model selection, as well as providing a wide array of posterior model summaries. We prescribe Bayesian residuals and methods for cross-validation and model selection for Poisson processes, log-Gaussian Cox processes, Gibbs processes, and cluster processes. These novel approaches are demonstrated using existing datasets and simulation studies.</p> === Dissertation