Objective Bayesian Analysis of Geometrically Anisotropic Spatial Data

• Activity Number: 289
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Hannes Kazianka*+
• Companies: Austrian Central Bank
• Keywords: Gaussian process ; geometric anisotropy ; Jeffreys prior ; reference prior ; nugget effect ; posterior propriety

Abstract

Berger et al. (2000) and Paulo (2005) developed default priors for regression, variance and range parameters of isotropic Gaussian random fields. Their work was extended by Kazianka and Pilz (2012) to also include a nugget parameter accounting for microscale variation and measurement error. To departure from isotropy, geometrically anisotropic models are often used in spatial statistics to analyze spatially referenced data. Within a Bayesian framework we develop default priors for the geometrically anisotropic Gaussian random field model including a nugget parameter. We present the Jeffreys prior and the reference prior and discuss how sample size and sampling design affect these priors. Moreover, we study posterior propriety and obtain that the predictive distribution at an ungauged location has 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 datasets for which we discuss correlation model choice as well as predictions and uncertainty estimates.