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Objective Bayesian analysis for CAR models

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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.

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Acknowledgments

D. Sun’s research was supported partially by the National Science Foundation grants SES-0720229, SES-1024080, and DMS-1007874. The authors would like to thank the editor, the associate editor, and anonymous referees for constructive comments to the earlier versions of the paper.

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Authors and Affiliations

  1. Department of Plant Science, South Dakota State University, Brookings, SD, 57007, USA

    Cuirong Ren

  2. School of Finance and Statistics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, China

    Dongchu Sun

  3. Department of Statistics, University of Missouri-Columbia, Columbia, MO,  65211, USA

    Dongchu Sun

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  1. Cuirong Ren
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  2. Dongchu Sun
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Correspondence to Cuirong Ren.

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Ren, C., Sun, D. Objective Bayesian analysis for CAR models. Ann Inst Stat Math 65, 457–472 (2013). https://doi.org/10.1007/s10463-012-0377-6

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  • DOI: https://doi.org/10.1007/s10463-012-0377-6

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