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Bayesian linear regression with skew‐symmetric error distributions with applications to survival analysis
Author(s) -
Rubio Francisco J.,
Genton Marc G.
Publication year - 2016
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6897
Subject(s) - prior probability , frequentist inference , univariate , bayesian linear regression , bayesian probability , econometrics , skew , context (archaeology) , statistics , computer science , regression analysis , bayesian multivariate linear regression , linear regression , posterior probability , accelerated failure time model , multivariate statistics , mathematics , bayesian inference , survival analysis , telecommunications , paleontology , biology
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. Copyright © 2016 John Wiley & Sons, Ltd.