Study Compression with Different New Prior distribution in Tobit Quantile Regression

Abstract

Bayesian estimation requires sampling from the posterior distributions. Where, the prior distributions are play a vital role in obtaining the simplifying the derivation of full conditional distributions, making Gibbs sampling algorithms more efficient. using the Laplace prior distribution (also known as the Double Exponential prior) is indeed a great choice in Bayesian Tobit quantile  regression for both variable selection and parameter estimation simultaneously. The Laplace prior has become popular in regression models because of its ability to induce sparsity in the estimated coefficients, which is particularly beneficial for variable selection. However, directly using the Laplace prior distribution is a very complex task when building the hierarchical model. To overcome  this issue, a set of transformations of the Laplace prior distribution has been used, which provide us with hierarchical models with more efficiency. In this paper, we will compare the transformations of the Laplace prior distribution that provide us with efficient estimators capable of generalization.