A matching prior for the shape parameter of the skew-normal distribution

CABRAS, STEFANO;Castellanos Nueda ME;RACUGNO, WALTER;Ventura L.

2012-01-01

---

Abstract

This paper deals with the issue of perform- ing a default Bayesian analysis on the shape parameter of the skew-normal distribution. Our approach is based on a suit- able pseudo-likelihood function and a matching prior distri- bution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoreti- cal perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance pa- rameters and the computation of multidimensional integrals.