Canadian Journal of Statistics

Objective Bayesian analysis of spatial models with separable correlation functions

Journal Article

Abstract

This paper considers general linear models for Gaussian geostatistical data with multi‐dimensional separable correlation functions involving multiple parameters. We derive various objective priors, such as the Jeffreys‐rule, independence Jeffreys, and usual and exact reference priors for the model parameters. In addition, we relax and simplify the assumptions in Paulo (2005) for the propriety of the posteriors in the general setup. We show that the frequentist coverage of posterior credible intervals for a function of range parameters do not depend on the regression coefficient or error variance. These objective priors and a proper flat prior based on ML estimates are compared by examining the frequentist coverage of equal‐tailed Bayesian credible intervals. An illustrative example is given from the field of complex computer model validations. The Canadian Journal of Statistics 41: 488–507; 2013 © 2013 Statistical Society of Canada

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