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dc.contributor.advisorHuang, Jianhua
dc.contributor.advisorSang, Huiyan
dc.creatorZhang, Bohai
dc.date.accessioned2020-02-28T16:06:47Z
dc.date.available2020-02-28T16:06:47Z
dc.date.created2015-08
dc.date.issued2015-08-10
dc.date.submittedAugust 2015
dc.identifier.urihttps://hdl.handle.net/1969.1/187445
dc.description.abstractClassical statistical models encounter the computational bottleneck for large spatial/spatio-temporal datasets. This dissertation contains three articles describing computationally efficient approximation methods for applying Gaussian process models to large spatial and spatio-temporal datasets. The first article extends the FSA-Block approach in [60] in the sense of preserving more information of the residual covariance matrix. By using a block conditional likelihood approximation to the residual likelihood, the residual covariance of neighboring data blocks can be preserved, which relaxes the conditional independence assumption of the FSA-Block approach. We show that the approximated likelihood by the proposed method is Gaussian with an explicit form of covariance matrix, and the computational complexity is linear with sample size n. We also show that the proposed method can result in a valid Gaussian process so that both the parameter estimation and prediction are consistent in the same model framework. Since neighborhood information are incorporated in approximating the residual covariance function, simulation studies show that the proposed method can further alleviate the mismatch problems in predicting responses on block boundary locations. The second article is the spatio-temporal extension of the FSA-Block approach, where we model the space-time responses as realizations from a Gaussian process model of spatio-temporal covariance functions. Since the knot number and locations are crucial to the model performance, a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed to select knots automatically from a discrete set of spatio-temporal points for the proposed method. We show that the proposed knot selection algorithm can result in more robust prediction results. Then the proposed method is compared with weighted composite likelihood method through simulation studies and an ozone dataset. The third article applies the nonseparable auto-covariance function to model the computer code outputs. It proposes a multi-output Gaussian process emulator with a nonseparable auto-covariance function to avoid limitations of using separable emulators. To facilitate the computation of nonseparable emulator, we introduce the FSA-Block approach to approximate the proposed model. Then we compare the proposed method with Gaussian process emulator with separable covariance models through simulated examples and a real computer code.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectSpatial statisticsen
dc.subjectspatio-temporal statisticsen
dc.subjectGaussian processen
dc.subjectcovariance matrixen
dc.subjectconditional likelihooden
dc.subjectuncertainty quantificationen
dc.titleStatistical Methods for Large Spatial and Spatio-temporal Datasetsen
dc.typeThesisen
thesis.degree.departmentStatisticsen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorTexas A&M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberJun, Mikyoung
dc.contributor.committeeMemberZhang, Renyi
dc.type.materialtexten
dc.date.updated2020-02-28T16:06:47Z
local.etdauthor.orcid0000-0002-9988-3215


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