BAYESIAN ANALYSIS OF CONDITIONAL AUTORIEGRESSIVE MODELS

Victor De Oliveira
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Victor De Oliveira: The University of Texas at San Antonio

No 95, Working Papers from College of Business, University of Texas at San Antonio

Abstract: Conditionally autoregressive (CAR) models have been extensively used for the analysis of spatial data in diverse areas, such as demography, economy, epidemiology and geography, as models for both latent and observed variables. In the latter case, the most common inferential method has been maximum likelihood, and the Bayesian approach has not been used much. This work proposes default (automatic) Bayesian analyses of CAR models. Two versions of Jereys prior, the independence Jereys and Jereys rule priors, are derived for the parameters of CAR models and properties of the priors and resulting posterior distributions are obtained. The two priors and their respective posteriors are compared based on simulated data. Also, frequentist properties of inferences based on maximum likelihood are compared with those based on the Jereys priors and the uniform prior. Finally, the proposed Bayesian analysis is illustraded by tting a CAR model to a phosphate dataset from an archeological region.

Keywords: CAR model; Eigenvalues and eigenvectors; Frequentist properties; Integrated likelihood; Maximum likelihood; Spatial data; Weight matrix. (search for similar items in EconPapers)
JEL-codes: C11 C31 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2009-06-24
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