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Prior distributions for variance parameters in ...
Bayesian Analysis (2006)1, Number 3, pp. 515 533 Prior distributions for variance parameters inhierarchical modelsAndrew GelmanDepartment of Statistics and Department of Political ScienceColumbia noninformative Prior distributions have been suggested forscale parameters in hierarchical models. We construct a newfolded-noncentral-tfamily of conditionally conjugate priors for hierarchicalstandard deviation pa-rameters, and then consider noninformative and weakly informative priors in thisfamily. We use an example to illustrate serious problems with the inverse-gammafamily of noninformative Prior distributions .
Hierarchical (multilevel) models are central to modern Bayesian statistics for both conceptual and practical reasons. On the theoretical side, hierarchical models allow a more “objective” approach to inference by estimating the parameters of prior distribu-tions from data rather than requiring them to be specified using subjective information
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