KAUST Grant NumberKUS-C1-016-04
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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.
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.
SponsorsMikyoung 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.