Journal
JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
Volume 18, Issue 4, Pages 514-537Publisher
SPRINGER
DOI: 10.1007/s13253-013-0137-y
Keywords
Gaussian process; Geometric anisotropy; Jeffreys prior; Nugget effect; Posterior propriety; Reference prior
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Anisotropic models are often used in spatial statistics to analyze spatially referenced data. Within a Bayesian framework we develop default priors for the anisotropic Gaussian random field model with and without including a nugget parameter accounting for the effects of microscale variations and measurement errors. We present Jeffreys priors and a reference prior and study their posterior propriety. Moreover, we obtain that the predictive distributions at ungauged locations have finite variance. We also show that the seemingly uninformative uniform prior for the anisotropy parameters, ratio and angle, yields an improper posterior. Finally, we find that the proposed priors have good frequentist properties and we illustrate our approach by analyzing two data sets for which we discuss model choice as well as predictions and uncertainty estimates.
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