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Prior distributions for variance parameters in hierarchical models

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  • Andrew Gelman

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.

Suggested Citation

  • Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," EERI Research Paper Series EERI_RP_2004_06, Economics and Econometrics Research Institute (EERI), Brussels.
    • Handle: RePEc:eei:rpaper:eeri_rp_2004_06
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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2004_06.pdf
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    References listed on IDEAS

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    1. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    2. 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:

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    2. repec:jss:jstsof:14:i05 is not listed on IDEAS
    3. Di Zhang & Qiang Niu & Youzhou Zhou, 2022. "Modeling Randomly Walking Volatility with Chained Gamma Distributions," Papers 2207.01151, arXiv.org, revised Oct 2022.
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    5. 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.
    6. repec:jss:jstsof:14:i14 is not listed on IDEAS

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    More about this item

    Keywords

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

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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