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Prior distributions for variance parameters in hierarchical models

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  • Andrew Gelman

    (Department of Statistics, Columbia University)

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," Econometrics 0404001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0404001
    Note: Type of Document - pdf; pages: 13
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0404/0404001.pdf
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    References listed on IDEAS

    as
    1. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    2. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
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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. 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.
    4. Junming Li & Xiulan Han & Xiao Li & Jianping Yang & Xuejiao Li, 2018. "Spatiotemporal Patterns of Ground Monitored PM 2.5 Concentrations in China in Recent Years," IJERPH, MDPI, vol. 15(1), pages 1-15, January.
    5. Crainiceanu, Ciprian M. & Ruppert, David & Wand, Matthew P., 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i14).
    6. 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.
    7. 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;
    All these keywords.

    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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