Abstract: The Bayesian bootstrap for doubly censored data is constructed from the empirical likelihood perspective, and a Gibbs sampler algorithm is proposed for evaluating the Bayesian bootstrap posterior. The proposed Bayesian bootstrap posterior is shown to be the limit of the nonparametric posteriors with Dirichlet process priors as the prior information vanishes, and to be equivalent to the weighted bootstrap on the observables. A small simulation study shows that the proposed Bayesian bootstrap estimator compares favorably with the nonparametric maximum likelihood estimator; furthermore its asymptotic properties are studied.
Key words and phrases: Bayesian bootstrap, doubly censored data, empirical likelihood, survival model.