Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2016-02-09
Print Publication Date2016-06-30
Permanent link to this recordhttp://hdl.handle.net/10754/600716
MetadataShow full item record
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.
CitationBayesian linear regression with skew-symmetric error distributions with applications to survival analysis 2016:n/a Statistics in Medicine
SponsorsWe 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).
JournalStatistics in Medicine
- Bayesian inference on mixed-effects location scale models with skew-t distribution and mismeasured covariates for longitudinal data.
- Authors: Lu T
- Issue date: 2017 Jul 20
- Semiparametric Bayesian inference on skew-normal joint modeling of multivariate longitudinal and survival data.
- Authors: Tang AM, Tang NS
- Issue date: 2015 Feb 28
- Bayesian bivariate linear mixed-effects models with skew-normal/independent distributions, with application to AIDS clinical studies.
- Authors: Huang Y, Chen R, Dagne G, Zhu Y, Chen H
- Issue date: 2015
- Bayesian analysis of multivariate mixed models for a prospective cohort study using skew-elliptical distributions.
- Authors: Kazemi I, Mahdiyeh Z, Mansourian M, Park JJ
- Issue date: 2013 Jul
- Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads.
- Authors: Bandyopadhyay D, Lachos VH, Castro LM, Dey DK
- Issue date: 2012 May