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Prior distributions for variance parameters in hierarchical models

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  • Andrew Gelman
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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://www.eeri.eu/documents/wp/EERI_RP_2004_06.pdf
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    Bibliographic Info

    Paper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2004_06.

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    Length: 14 pages
    Date of creation: Jun 2004
    Date of revision:
    Handle: RePEc:eei:rpaper:eeri_rp_2004_06

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    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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    Cited by:
    1. 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).
    2. 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).
    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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