Bayesian Inference for the Multivariate Extended-Skew Normal Distribution

TL;DR

This paper introduces a Bayesian sequential Monte Carlo method for estimating the multivariate extended skew-normal distribution, which effectively models skewed and heavy-tailed data, and demonstrates its performance through simulations and real data analysis.

Contribution

It develops a novel Bayesian SMC approach for the extended skew-normal distribution, including prior elicitation and application to sample selection models.

Findings

SMC sampler performs well in simulations

Provides new insights into distribution parametrizations

Successfully applied to real datasets

Abstract

The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and marginalization. In this paper we propose a Bayesian computational approach based on a sequential Monte Carlo (SMC) sampler to estimate such distributions. The practical implementation of each step of the algorithm is discussed and the elicitation of prior distributions takes into consideration some unusual behaviour of the likelihood function and the corresponding Fisher information matrix. Using Monte Carlo simulations, we provide strong evidence regarding the performances of the SMC sampler as well as some new insights regarding the parametrizations of the extended skew-normal distribution. A generalization to the extended skew-normal sample selection model is also presented. Finally we proceed with the analysis of two real datasets.