TY - CHAP

T1 - Mixed-effects modelling of Kevlar fibre failure times through Bayesian non-parametrics

AU - Mantovan, P

AU - Secchi, P

AU - Argiento, Raffaele

AU - Guglielmi, A

AU - Pievatolo, A

PY - 2010

Y1 - 2010

N2 - We examine the accelerated failure time model for univariate data with right censoring, with application to failure times of Kevlar fibres grouped by spool, subject to different stress levels. We propose a semi-parametric modelling by letting the error distribution be a shape-scale mixture of Weibull densities, the mixing measure being a normalised generalised gamma measure. We obtain posterior estimates of the regression parameter and also of credibility intervals for the predictive distributions and their quantiles, by including the posterior distribution of the random mixing probability in the MCMC scheme. The number of components in the non-parametric mixture can be interpreted as the number of groups, having a prior distribution induced by the non-parametric model, and is inferred from the data. Compared to previous results, we obtain narrower interval estimates of the quantiles of the predictive survival function. Other diagnostic plots, such as predictive tail probabilities and Bayesian residuals, show a good agreement between the model and the data.

AB - We examine the accelerated failure time model for univariate data with right censoring, with application to failure times of Kevlar fibres grouped by spool, subject to different stress levels. We propose a semi-parametric modelling by letting the error distribution be a shape-scale mixture of Weibull densities, the mixing measure being a normalised generalised gamma measure. We obtain posterior estimates of the regression parameter and also of credibility intervals for the predictive distributions and their quantiles, by including the posterior distribution of the random mixing probability in the MCMC scheme. The number of components in the non-parametric mixture can be interpreted as the number of groups, having a prior distribution induced by the non-parametric model, and is inferred from the data. Compared to previous results, we obtain narrower interval estimates of the quantiles of the predictive survival function. Other diagnostic plots, such as predictive tail probabilities and Bayesian residuals, show a good agreement between the model and the data.

KW - accelerated failure time regression models Bayesian semiparametrics MCMC algorithms mixed-effects models mixture models Weibull distribution

KW - accelerated failure time regression models Bayesian semiparametrics MCMC algorithms mixed-effects models mixture models Weibull distribution

UR - http://hdl.handle.net/10807/155932

UR - https://doi.org/10.1007/978-88-470-1386-5_2

U2 - 10.1007/978-88-470-1386-5_2

DO - 10.1007/978-88-470-1386-5_2

M3 - Chapter

SN - 9788847013858

SP - 13

EP - 26

BT - Complex Data Modeling and Computationally Intensive Statistical Methods

ER -