Flexible objective Bayesian linear regression with applications in survival analysis

TL;DR

This paper develops an objective Bayesian linear regression approach using two-piece scale mixtures of normal distributions, enabling flexible modeling of errors in survival analysis, with demonstrated good frequentist properties and real-data applications.

Contribution

It introduces a noninformative prior for Bayesian linear regression with flexible error distributions, extending previous models to censored data in survival analysis.

Findings

Posterior credible intervals have good frequentist coverage.

Models perform well on real survival data.

Propriety of the posterior is established under broad conditions.

Abstract

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual assumption of normality of the errors in terms of heavy tails, asymmetry, and certain types of heteroscedasticity. We propose a general noninformative, scale-invariant, prior structure and provide sufficient conditions for the propriety of the posterior distribution of the model parameters, which cover cases when the response variables are censored. These results allow us to apply the proposed models in the context of survival analysis. This paper represents an extension to the Bayesian framework of the models proposed in Rubio and Hong (2015). We present a simulation study that shows good frequentist properties of the posterior credible intervals as well as point estimators associated to the proposed priors. We illustrate the performance of these models with real data in the context of survival analysis of cancer patients.