Inference in Two-Piece Location-Scale Models with Jeffreys Priors

This paper addresses the use of Jeffreys priors in the context of univariate threeparameter location-scale models, where skewness is introduced by differing scale parameters either side of the location. We focus on various commonly used parameterizations for these models. Jeffreys priors are shown not to allow for posterior inference in the wide and practically relevant class of distributions obtained by skewing scale mixtures of normals. Easily checked conditions under which independence Jeffreys priors can be used for valid inference are derived. We empirically investigate the posterior coverage for a number of Bayesian models, which are also used to conduct inference on real data.