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 Abstract
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. |