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

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    1601.02224.pdf
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    Type
    Article
    Authors
    Rubio, Francisco J.
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2016-02-09
    Online Publication Date
    2016-02-09
    Print Publication Date
    2016-06-30
    Permanent link to this record
    http://hdl.handle.net/10754/600716
    
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    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.
    Citation
    Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis 2016:n/a Statistics in Medicine
    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).
    Publisher
    Wiley
    Journal
    Statistics in Medicine
    DOI
    10.1002/sim.6897
    PubMed ID
    26856806
    arXiv
    1601.02224
    Additional Links
    http://doi.wiley.com/10.1002/sim.6897
    ae974a485f413a2113503eed53cd6c53
    10.1002/sim.6897
    Scopus Count
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    Articles; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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