Semi- and non-parametric Bayesian analysis of duration models with Dirichlet priors: A survey

The object of this paper is to review the main results obtained in semi- an d non-parametric Bayesian analysis of duration models. Standard nonparametr ic Bayesian models for independent and identically distributed observations are reviewed in line with Ferguson's pioneering papers. Recent results on the characterization of Dirichlet processes and on nonparametric treatment of censoring and of heterogeneity in the context of mixtures of Dirichlet p rocesses are also discussed. The final section considers a Bayesian semipar ametric version of the proportional hazards model.