Natural (non-)informative priors for skew-symmetric distributions

TL;DR

This paper introduces a novel approach for constructing proper priors for the skewness parameter in skew-symmetric distributions, utilizing Total Variation distance to encode prior beliefs and improve Bayesian inference.

Contribution

It proposes a new method for defining priors based on the perturbation effect measured by Total Variation, enhancing prior informativeness and posterior properties in skew-symmetric models.

Findings

Noninformative priors have good frequentist properties similar to Jeffreys prior.

Informative priors outperform existing methods in the literature.

Proposed priors are scale- and location-invariant and ensure posterior propriety.

Abstract

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew-symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the Total Variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our noninformative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale- and location-invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data.