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 . We suggest instead to use a uni-form Prior on the hierarchical standard deviation, using the half-tfamily when thenumber of groups is small and in other settings where a weaklyinformative prioris desired.

Fully-Bayesian analyses of hierarchical linear models have been considered for at least forty years (Hill, 1965, Tiao and Tan, 1965, and Stone and Springer, 1965) and have ... We shall work with a simple two-level normal model of data yij with group-level effects

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  Linear, Model, Levels, Hierarchical, Hierarchical linear models

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