Asymmetric Two-Piece Multiple Linear Regression Model based on the Scale Mixture of Normal Family;Bayesian Framework

Abstract

The main object of this article is to discuss Bayesian methodology for linear regression model according to the class of two-piece scale mixture of normal distribution. This model is appropriate for capturing departure from the usual normal assumption of error such as heavy tails, asymmetric and types of heteroscedasticity. Linear regression model is used to analyze data based on the normality assumption. The robust inference for normality assumption as a way to replace the Gaussian assumption for the residual errors with two-piece scale mixture of normal distribution is a Bayesian framework. An efficient way for applying Bayesian methodology is introduced using Markov chain Monte Carlo (MCMC) algorithm as a way to specify the posterior inference which has been used.