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

Francisco J. Rubio, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 noninformative 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 with 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 Information.
Original languageEnglish (US)
Pages (from-to)2441-2454
Number of pages14
JournalStatistics in Medicine
Volume35
Issue number14
DOIs
StatePublished - Feb 9 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank an Associate Editor and two referees for their very helpful comments. FJR gratefully acknowledges research support from EPSRC grant EP/K007521/1. MGG's research is supported by King Abdullah University of Science and Technology (KAUST).

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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