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Assessing fit in Bayesian models for spatial processes
Author(s) -
Jun M.,
Katzfuss M.,
Hu J.,
Johnson V. E.
Publication year - 2014
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2315
Subject(s) - goodness of fit , markov chain monte carlo , covariance , bayesian probability , computer science , statistics , gaussian , gaussian process , random field , mathematics , monte carlo method , algorithm , statistical physics , physics , quantum mechanics
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. Copyright © 2014 John Wiley & Sons, Ltd.