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Objective Bayesian analysis for CAR models

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  • Cuirong Ren
  • Dongchu Sun

Abstract

Objective priors, especially reference priors, have been studied extensively for spatial data in the last decade. In this paper, we study objective priors for a CAR model. In particular, the properties of the reference prior and the corresponding posterior are studied. Furthermore, we show that the frequentist coverage probabilities of posterior credible intervals depend only on the spatial dependence parameter $$\rho $$ , and not on the regression coefficient or the error variance. Based on the simulation study for comparing the reference and Jeffreys priors, the performance of two reference priors is similar and better than the Jeffreys priors. One spatial dataset is used for illustration. Copyright The Institute of Statistical Mathematics, Tokyo 2013

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  • Cuirong Ren & Dongchu Sun, 2013. "Objective Bayesian analysis for CAR models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 457-472, June.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:3:p:457-472
    DOI: 10.1007/s10463-012-0377-6
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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. Victor Oliveira, 2012. "Bayesian analysis of conditional autoregressive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 107-133, February.
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    Cited by:

    1. Ren, Cuirong & Sun, Dongchu, 2014. "Objective Bayesian analysis for autoregressive models with nugget effects," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 260-280.

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