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Bayesian Analysis of Spatial Point Patterns

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Date
2014
Author
Leininger, Thomas Jeffrey
Advisor
Gelfand, Alan E
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Abstract

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.

Type
Dissertation
Department
Statistical Science
Subject
Statistics
cross-validation
Gibbs process
Log-Gaussian Cox process
model selection
point pattern residuals
Poisson process
Permalink
https://hdl.handle.net/10161/8730
Citation
Leininger, Thomas Jeffrey (2014). Bayesian Analysis of Spatial Point Patterns. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/8730.
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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

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