摘要：We put forward the Scaled Beta2 (SBeta2) as a flexible and tractable family for modeling scales in both hierarchical and non-hierarchical settings. Various sensible alternatives to the overuse of vague Inverted Gamma priors have been proposed, mainly for hierarchical models. Several of these alternatives are particular cases of the SBeta2 or can be well approximated by it. This family of distributions can be obtained in closed form as a Gamma scale mixture of Gamma distributions, as the Student distribution can be obtained as a Gamma scale mixture of Normal variables. Members of the SBeta2 family arise as intrinsic priors and as divergence based priors in diverse situations, hierarchical and non-hierarchical.
