Hierarchical Gaussian Processes for Spatially Dependent Model Selection

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dc.contributor.authorFry, James Thomasen
dc.contributor.committeechairLeman, Scotland C.en
dc.contributor.committeememberResler, Lynn M.en
dc.contributor.committeememberGramacy, Robert B.en
dc.contributor.committeememberSmith, Eric P.en
dc.contributor.departmentStatisticsen
dc.date.accessioned2018-07-19T08:00:32Zen
dc.date.available2018-07-19T08:00:32Zen
dc.date.issued2018-07-18en
dc.description.abstractIn this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:16674en
dc.identifier.urihttp://hdl.handle.net/10919/84161en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectspatial statisticsen
dc.subjectGaussian processen
dc.subjectmodel selectionen
dc.subjectnonstationary processen
dc.subjectIsing distributionen
dc.subjectCAR modelen
dc.titleHierarchical Gaussian Processes for Spatially Dependent Model Selectionen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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