[Accepted Manuscript] Flexible objective Bayesian linear regression with applications in survival analysis


Rubio, F.J.; Yu, K.; (2016) [Accepted Manuscript] Flexible objective Bayesian linear regression with applications in survival analysis. Journal of applied statistics. ISSN 0266-4763 DOI: https://doi.org/10.1080/02664763.2016.1182138 (In Press)

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Abstract

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual assumption of normality of the errors in terms of heavy tails, asymmetry, and certain types of heteroscedasticity. We propose a general non-informative, scale-invariant, prior structure and provide sufficient conditions for the propriety of the posterior distribution of the model parameters, which cover cases when the response variables are censored. These results allow us to apply the proposed models in the context of survival analysis. This paper represents an extension to the Bayesian framework of the models proposed in [16]. We present a simulation study that shows good frequentist properties of the posterior credible intervals as well as point estimators associated to the proposed priors. We illustrate the performance of these models with real data in the context of survival analysis of cancer patients.

Item Type: Article
Faculty and Department: Faculty of Epidemiology and Population Health > Dept of Non-Communicable Disease Epidemiology
URI: http://researchonline.lshtm.ac.uk/id/eprint/3141147

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