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Bayesian Analysis Of Conditional Autoriegressive Models

Author

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  • Victor De Oliveira

    (The 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.

Suggested Citation

  • Victor De Oliveira, 2009. "Bayesian Analysis Of Conditional Autoriegressive Models," Working Papers 0095, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:00123mss
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    File URL: http://interim.business.utsa.edu/wps/MSS/0095MSS-496-2009.pdf
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    References listed on IDEAS

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    1. Berger J.O. & De Oliveira V. & Sanso B., 2001. "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1361-1374, December.
    2. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    3. A. F. Militino & M. D. Ugarte & L. García-Reinaldos, 2004. "Alternative Models for Describing Spatial Dependence among Dwelling Selling Prices," The Journal of Real Estate Finance and Economics, Springer, vol. 29(2), pages 193-209, September.
    4. Case, Anne C. & Rosen, Harvey S. & Hines, James Jr., 1993. "Budget spillovers and fiscal policy interdependence : Evidence from the states," Journal of Public Economics, Elsevier, vol. 52(3), pages 285-307, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    CAR model; Eigenvalues and eigenvectors; Frequentist properties; Integrated likelihood; Maximum likelihood; Spatial data; Weight matrix.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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