Objective Bayesian Analysis of Spatially Correlated Data
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- 1 December 2001
- journal article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 96 (456) , 1361-1374
- https://doi.org/10.1198/016214501753382282
Abstract
Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) with a small number of unknown parameters. We consider objective Bayesian analysis of such spatial models, when the mean function of the Gaussian random field is specified as in a linear model. It is thus necessary to determine an objective (or default) prior distribution for the unknown mean and covariance parameters of the random field. We first show that common choices of default prior distributions, such as the constant prior and the independent Jeffreys prior, typically result in improper posterior distributions for this model. Next, the reference prior for the model is developed and is shown to yield a proper posterior distribution. A further attractive property of the reference prior is that it can be used...Keywords
This publication has 17 references indexed in Scilit:
- Comment on Perlman and Wu, “The Emperor’s new tests” (with rejoinder by authors)Statistical Science, 1999
- Bayesian Prediction of Transformed Gaussian Random FieldsJournal of the American Statistical Association, 1997
- Bayesian Variogram Modeling for an Isotropic Spatial ProcessJournal of Agricultural, Biological and Environmental Statistics, 1997
- The Selection of Prior Distributions by Formal RulesJournal of the American Statistical Association, 1996
- The Intrinsic Bayes Factor for Model Selection and PredictionJournal of the American Statistical Association, 1996
- An Approach to Statistical Spatial-Temporal Modeling of Meteorological FieldsJournal of the American Statistical Association, 1994
- A Bayesian Analysis of KrigingTechnometrics, 1993
- Fitting Continuous ARMA Models to Unequally Spaced Spatial DataJournal of the American Statistical Association, 1993
- Estimating a Product of Means: Bayesian Analysis with Reference PriorsJournal of the American Statistical Association, 1989
- Bayesian inference for variance components using only error contrastsBiometrika, 1974