Handle URI:
http://hdl.handle.net/10754/597609
Title:
Assessing fit in Bayesian models for spatial processes
Authors:
Jun, M.; Katzfuss, M.; Hu, J.; Johnson, V. E.
Abstract:
© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.
Citation:
Jun M, Katzfuss M, Hu J, Johnson VE (2014) Assessing fit in Bayesian models for spatial processes. Environmetrics 25: 584–595. Available: http://dx.doi.org/10.1002/env.2315.
Publisher:
Wiley-Blackwell
Journal:
Environmetrics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
16-Sep-2014
DOI:
10.1002/env.2315
Type:
Article
ISSN:
1180-4009
Sponsors:
Mikyoung Jun's research was supported by NSF grant DMS-0906532. Mikyoung Jun also acknowledges that this publication is based in part on work supported by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). Jianhua Hu's research was partially supported by NSF grant DMS-0706818, NIH grants R01GM080503-01A1, R21CA129671, and NCI CA97007. Valen Johnson's research was supported by NIH grant R01 CA158113. The authors thank Chris Paciorek for providing the posterior samples used in Section 4.1.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorJun, M.en
dc.contributor.authorKatzfuss, M.en
dc.contributor.authorHu, J.en
dc.contributor.authorJohnson, V. E.en
dc.date.accessioned2016-02-25T12:42:59Zen
dc.date.available2016-02-25T12:42:59Zen
dc.date.issued2014-09-16en
dc.identifier.citationJun M, Katzfuss M, Hu J, Johnson VE (2014) Assessing fit in Bayesian models for spatial processes. Environmetrics 25: 584–595. Available: http://dx.doi.org/10.1002/env.2315.en
dc.identifier.issn1180-4009en
dc.identifier.doi10.1002/env.2315en
dc.identifier.urihttp://hdl.handle.net/10754/597609en
dc.description.abstract© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.en
dc.description.sponsorshipMikyoung Jun's research was supported by NSF grant DMS-0906532. Mikyoung Jun also acknowledges that this publication is based in part on work supported by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). Jianhua Hu's research was partially supported by NSF grant DMS-0706818, NIH grants R01GM080503-01A1, R21CA129671, and NCI CA97007. Valen Johnson's research was supported by NIH grant R01 CA158113. The authors thank Chris Paciorek for providing the posterior samples used in Section 4.1.en
dc.publisherWiley-Blackwellen
dc.subjectBayesian p-valueen
dc.subjectCovariance functionen
dc.subjectGaussian random fielden
dc.subjectGoodness-of-fit testen
dc.subjectPivotal quantityen
dc.titleAssessing fit in Bayesian models for spatial processesen
dc.typeArticleen
dc.identifier.journalEnvironmetricsen
dc.contributor.institutionDepartment of Statistics; Texas A&M University; College Station TX U.S.A.en
dc.contributor.institutionDepartment of Biostatistics; UT MD Anderson Cancer Center; Houston TX U.S.A.en
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.