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Prior distributions for variance parameters in hierarchical models

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Author Info
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.

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Paper provided by Economics and Econometrics Research Institute (EERI) 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;

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: 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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  1. 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. [Downloadable!]
  2. Cabrini, Silvina & Irwin, Scott & Good, Darrel, 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). [Downloadable!]
  3. Matthew P. Wand & David Ruppert & Ciprian M. Crainiceanu, 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, American Statistical Association, vol. 14(14), 09. [Downloadable!]
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