Bayesian Variable Selection for Skewed Heteroscedastic Response

TL;DR

This paper introduces Bayesian variable selection methods tailored for skewed, heteroscedastic data, enabling accurate median and quantile estimation, with proven asymptotic predictor selection and practical handling of large errors.

Contribution

It presents novel Bayesian procedures that improve variable selection and estimation in complex heteroscedastic, skewed models, including extensions for large error observations.

Findings

Effective estimation of median and quantiles in skewed data

Asymptotic selection of true predictors with increasing covariates

Practical advantages demonstrated through simulations and medical data analysis

Abstract

In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate the median and other quantile functions, accommodate non-local prior for regression effects without compromising ease of implementation via sampling based tools, and asymptotically select the true set of predictors even when the number of covariates increases in the same order of the sample size. We also extend our method to deal with some observations with very large errors. Via simulation studies and a re-analysis of a medical cost study with large number of potential predictors, we illustrate the ease of implementation and other practical advantages of our approach compared to existing methods for such studies.