Round table MATHMET

5th edition of the Mathmet international conference, Paris, France, 2-4 November 2022.Contribution to the Strategic Research Agenda of MATHMET from the point of view of Technical Committee for Photometry and Radiometry of EURAME

Mixed-effects modelling of Kevlar fibre failure times throughBayesian nonparametrics.

We examine the accelerated failure time model for univariate failure time data with right censoring, with application to the failure times of Kevlar fibres from different spools, 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 normalized generalized gamma measure. We obtain posterior estimates of the regression parameter and also of credibility intervals for the predictive distributions and their quantiles, by including in the MCMC scheme the posterior distribution of the random mixing probability. The number of components in the nonparametric mixture can be interpreted as the number of random effects, having a prior distribution induced by the nonparametric 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 tails and Bayesian residuals, show a good agreement between the model and the data