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Objective Bayesian analysis for autoregressive models with nugget effects

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  • Ren, Cuirong
  • Sun, Dongchu

Abstract

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been conducted recently, but the Bayesian approach has not used or explored these two models with nugget effects. In this paper, we consider general autoregressive models including both CAR and SAR models. The Jeffreys-rule, independence Jeffreys, commonly used reference and “exact” reference priors are derived. The propriety of the marginal priors and joint posteriors is studied for a large class of objective priors. Various Jeffreys and reference priors are shown to yield improper posteriors and only the Jeffreys-rule and the “exact” reference priors yield proper posteriors. We make comparisons for these two objective priors using the frequentist coverage probabilities of the credible intervals. An illustration is given using a real spatial data-set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:260-280
    DOI: 10.1016/j.jmva.2013.11.003
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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.
    3. 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.
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