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

Handle URI:
http://hdl.handle.net/10754/600716
Title:
Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis
Authors:
Rubio, Francisco J.; Genton, Marc G. ( 0000-0001-6467-2998 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis 2016:n/a Statistics in Medicine
Publisher:
Wiley-Blackwell
Journal:
Statistics in Medicine
Issue Date:
9-Feb-2016
DOI:
10.1002/sim.6897
Type:
Article
ISSN:
02776715
Sponsors:
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).
Additional Links:
http://doi.wiley.com/10.1002/sim.6897
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorRubio, Francisco J.en
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2016-03-07T13:00:33Zen
dc.date.available2016-03-07T13:00:33Zen
dc.date.issued2016-02-09en
dc.identifier.citationBayesian linear regression with skew-symmetric error distributions with applications to survival analysis 2016:n/a Statistics in Medicineen
dc.identifier.issn02776715en
dc.identifier.doi10.1002/sim.6897en
dc.identifier.urihttp://hdl.handle.net/10754/600716en
dc.description.abstractWe 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.en
dc.description.sponsorshipWe 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).en
dc.language.isoenen
dc.publisherWiley-Blackwellen
dc.relation.urlhttp://doi.wiley.com/10.1002/sim.6897en
dc.rightsThis is the peer reviewed version of the following article: Rubio, F. J., and Genton, M. G. (2016) Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis. Statist. Med., which has been published in final form at http://doi.wiley.com/10.1002/sim.6897. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.en
dc.titleBayesian linear regression with skew-symmetric error distributions with applications to survival analysisen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalStatistics in Medicineen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Statistics; University of Warwick; Coventry CV4 7AL U.K.en
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorGenton, Marc G.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.