Bayesian inference for scale mixtures of skew-normal linear models under the centered parameterization
Abstract
In many situations we are interested in modeling real data where the response distribution, even conditionally on the covariates, presents asymmetry and/or heavy/light tails. In these situations, it is more suitable to consider models based on the skewed and/or heavy/light tailed distributions, such as the class of scale mixtures of skew-normal distributions. The classical parameterization of this distributions may not be good due to the some inferential issues when the skewness parameter is in a neighborhood of 0, then, the centered parameterization becomes more appropriate. In this paper, we developed a class of scale mixtures of skew-normal distributions under the centered parameterization, also a linear regression model based on them was proposed. We explore a hierarchical representation and set up a MCMC scheme for parameter estimation. Furthermore, we developed residuals and influence analysis tools. A Monte Carlo experiment is conducted to evaluate the performance of the MCMC algorithm and the behavior of the residual distribution. The methodology is illustrated with the analysis of a real data set.
Cite
@article{arxiv.2406.03432,
title = {Bayesian inference for scale mixtures of skew-normal linear models under the centered parameterization},
author = {João Victor B. de Freitas and Caio L. N. Azevedo},
journal= {arXiv preprint arXiv:2406.03432},
year = {2024}
}