Bayesian variable selection and coefficient estimation in heteroscedastic linear regression model

In many real applications, such as econometrics, biological sciences, radio- immunoassay, finance, and medicine, the usual assumption of constant error variance may be unrealistic. Ignoring heteroscedasticity ( non- constant error variance), if it is present in the data, may lead to incorrect inferences and inefficient estimation. In this paper, a simple and effcient Gibbs sampling algorithm is proposed, based on a heteroscedastic linear regression model with an l1 penalty. Then, a Bayesian stochastic search variable selection method is proposed for subset selection. Simulations and real data examples are used to compare the performance of the proposed methods with other existing methods. The results indicate that the proposal performs well in the simulations and real data examples. R code is available upon request.