Question

Gelman's (2006) paper on noninformative prior distributions for variance parameters has attracted over 3,100 citations (Google scholar). The Half-t distribution introduced in that paper is now considered the "default" prior to use for any standard deviation parameter a) Show that if σ2 is generated from the following hierarchical model, a ~ Inv-Gamma(α-1/2, λ-1/A2), then the (positive) square root σ has a marginal Half-t(v, A) distribution with density Here, the "scale" A > 0 and "degrees-of-freedom" v > 0 are fixed hyperparameters.

Answer 1

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