Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis

TL;DR

This paper develops Bayesian linear regression models with skew-symmetric error distributions, allowing for asymmetry and heavy tails, and applies them to survival analysis with censored data, demonstrating good properties and real-data performance.

Contribution

It introduces a non-informative prior for skew-symmetric error models, proves posterior propriety under mild conditions, and extends results to censored survival data.

Findings

Posterior credible intervals have good frequentist coverage.

Models effectively capture asymmetry and heavy tails in data.

Extensions to multivariate responses are discussed in supplementary material.

Abstract

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general non-informative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. We extend these propriety results to cases where the response variables are censored. The latter scenario is of interest in the context of accelerated failure time models, which are relevant in survival analysis. We present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated to the proposed priors. This study also sheds some light on the trade-off between increased model flexibility and the risk of over-fitting. We illustrate the performance of the proposed models with real data. Although we focus on models with univariate response variables, we also present some extensions to the multivariate case in the Supporting Web Material.