Empirical Bayes Inference for Means Using Student t Prior Distributions

Hierarchical models for L studies, domains or experiments often assume that the study means have a common normal population distribution. However, modeling normal sampling distributions with a normal population distribution may overstate the level of exchangeability of the studies. Using heavy tailed population distributions, in particular t distributions, provide some protection from combining dissimilar studies, domains or experiments (Gelman, Carlin, Stern, and Rubin, 1995, O’Hagan, 1988).