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Objective Bayesian analysis of spatial models with separable correlation functions
Author(s) -
Ren Cuirong,
Sun Dongchu,
Sahu Sujit K.
Publication year - 2013
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11186
Subject(s) - frequentist inference , prior probability , bayesian probability , mathematics , statistics , range (aeronautics) , gaussian , variance (accounting) , econometrics , bayesian inference , materials science , physics , composite material , quantum mechanics , accounting , business
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