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Propriety of posterior in Bayesian space varying parameter models with normal data

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  • Rodrigues, Alexandre
  • Assunção, Renato

Abstract

In Bayesian spatially varying parameter models the covariates' coefficients in a regression model are allowed to change smoothly in space. A Markov random field is adopted as an improper prior distribution for the area-specific spatial effects. We demonstrate that the posterior distribution is a proper probability distribution.

Suggested Citation

  • Rodrigues, Alexandre & Assunção, Renato, 2008. "Propriety of posterior in Bayesian space varying parameter models with normal data," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2408-2411, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2408-2411
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    1. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
    2. A. Brezger & L. Fahrmeir & A. Hennerfeind, 2007. "Adaptive Gaussian Markov random fields with applications in human brain mapping," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 327-345, May.
    3. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    4. P. Congdon, 2003. "Modelling spatially varying impacts of socioeconomic predictors on mortality outcomes," Journal of Geographical Systems, Springer, vol. 5(2), pages 161-184, August.
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    Cited by:

    1. Peng Wei & Wei Pan, 2010. "Network‐based genomic discovery: application and comparison of Markov random‐field models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 105-125, January.

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