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Spatial models with applications in computer experiments

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dc.contributor.authorWang, Ke, author
dc.contributor.authorDavis, Richard A., advisor
dc.contributor.authorBreidt, F. Jay, advisor
dc.date.accessioned2024-03-13T20:28:03Z
dc.date.available2024-03-13T20:28:03Z
dc.date.issued2008
dc.description.abstractOften, a deterministic computer response is modeled as a realization from a, stochastic process such as a Gaussian random field. Due to the limitation of stationary Gaussian process (GP) in inhomogeneous smoothness, we consider modeling a deterministic computer response as a realization from a stochastic heteroskedastic process (SHP), a stationary non-Gaussian process. Conditional on a latent process, the SHP has non-stationary covariance function and is a non-stationary GP. As such, the sample paths of this process exhibit greater variability and hence offer more modeling flexibility than those produced by a, traditional GP model. We use maximum likelihood for inference in the SHP model, which is complicated by the high dimensionality of the latent process. Accordingly, we develop an importance sampling method for likelihood computation and use a low-rank kriging approximation to reconstruct the latent process. Responses at unobserved locations can be predicted using empirical best predictors or by empirical best linear unbiased predictors. In addition, prediction error variances are obtained. The SHP model can be used in an active learning context, adaptively selecting new locations that provide improved estimates of the response surface. Estimation, prediction, and adaptive sampling with the SHP model are illustrated with several examples. Our spatial model can be adapted to model the first partial derivative process. The derivative process provides additional information about the shape and smoothness of the underlying deterministic function and can assist in the prediction of responses at unobserved sites. The unconditional correlation function for the derivative process presents some interesting properties, and can be used as a new class of spatial correlation functions. For parameter estimation, we propose to use a similar strategy to develop an importance sampling technique to compute the joint likelihood of responses and derivatives. The major difficulties of bringing in derivative information are the increase in the dimensionality of the latent process and the numerical problems of inverting the enlarged covariance matrix. Some possible ways to utilize this information more efficiently are proposed.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Wang_2008_3332774.pdf
dc.identifier.urihttps://hdl.handle.net/10217/238012
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectadaptive sampling
dc.subjectcomputer experiments
dc.subjectinhomogeneity
dc.subjectlocal sensitivity
dc.subjectmetamodeling
dc.subjectspatial processes
dc.subjectstochastic heteroskedastic process
dc.subjectstatistics
dc.titleSpatial models with applications in computer experiments
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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