Bayesian analysis of progressively censored competing risks data

In this paper we consider the Bayesian inference of the unknown parameters of the progressively censored competing risks data, when the lifetime distributions are Weibull. It is assumed that the latent cause of failures have independent Weibull distributions with the common shape parameter, but different scale parameters. In this article, it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta-Dirichlet priors. When the common shape parameter is known, the Bayes estimates of the scale parameters have closed form expressions, but when the common shape parameter is unknown, the Bayes estimates do not have explicit expressions. In this case we propose to use MCMC samples to compute the Bayes estimates and highest posterior density (HPD) credible intervals. Monte Carlo simulations are performed to investigate the performances of the estimators. Two data sets are analyzed for illustration. Finally we provide a methodology to compare two different censoring schemes and thus find the optimum Bayesian censoring scheme.