Objective Bayesian Analysis of Spatial Data with Measurement Error
Victor De Oliveira
Department of Management Science and Statistics
The University of Texas at San Antonio
This talk provides the basis for default Bayesian analysis of Gaussian random fields based on geostatistical data that contain measurement error. A reference prior and two versions of Jeffreys prior are derived for the model parameters, and properties of the resulting posteriors in terms of propriety and existence of relevant moments are provided. Existence of the mean and variance of the predictive distributions based on the these default priors is established. The reference prior is obtained from a representation of the integrated likelihood that is particularly convenient for computation and analysis.
It is also shown that these default priors are not very sensitive to some aspects of the design and model, and have good frequentist properties. Finally, a dataset of carbon-nitrogen ratios from an agricultural field is used to illustrate the Bayesian analysis based on the reference prior.