Objective Bayesian Analysis of Spatially Correlated Data Including Measurement Error

• Activity Number: 657
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Hannes Kazianka*+ and Jürgen Pilz
• Companies: University of Klagenfurt and University Klagenfurt
• Keywords: Spatial Statistics ; Objective Bayesian Analysis ; Jeffreys Prior ; Spatial Extremes ; Copula

Abstract

Berger et al. (2000) developed default priors for unknown regression, variance and range parameters of Gaussian random fields. In this paper we extend their work and generalize the considered correlation functions to include a nugget effect, which corresponds to a measurement error. Following Paulo (2005), we derive the Jeffreys-rule prior, the independence Jeffreys prior and the reference prior and prove under which conditions they lead to a proper posterior distribution. We discuss how the sample size and the sampling design affect the priors. In a comparative study we compute the frequentist coverage of 95% Bayesian credible intervals and find that the reference prior shows the best performance. Finally, we use the methodology for Bayesian copula-based spatial modeling (Kazianka and Pilz, 2010) of extreme valued data and present the results obtained for different choices of priors.