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Prior distributions for variance parameters in hierarchical models

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Author Info

  • Andrew Gelman

    (Department of Statistics, Columbia University)

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    Abstract

    Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral- t family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of ``noninformative'' prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-t family when the number of groups is small and in other settings where a weakly informative prior is desired.

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    File URL: http://128.118.178.162/eps/em/papers/0404/0404001.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Econometrics with number 0404001.

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    Length: 13 pages
    Date of creation: 14 Apr 2004
    Date of revision:
    Handle: RePEc:wpa:wuwpem:0404001

    Note: Type of Document - pdf; pages: 13
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    Web page: http://128.118.178.162

    Related research

    Keywords: Bayesian inference; conditional conjugacy; folded noncentral-t distribution; half-t distribution; hierarchical model; multilevel model; noninformative prior distribution; weakly informative prior distribution;

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    References

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    1. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
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    Cited by:
    1. Ciprian M. Crainiceanu & David Ruppert & Matthew P. Wand, . "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, American Statistical Association, vol. 14(i14).
    2. Cabrini, Silvina M. & Irwin, Scott H. & Good, Darrel L., 2005. "Efficient Portfolios of Market Advisory Services: An Application of Shrinkage Estimators," 2005 Annual meeting, July 24-27, Providence, RI 19469, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Ciprian Crainiceanu & David Ruppert & Raymond Carroll, 2004. "Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1061, Berkeley Electronic Press.

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