A comparison of nonparametric priors in hierarchical mixture modelling of lifetime dat

We will pursue a Bayesian nonparametric approach in the hierarchical mixture modelling\r\nof lifetime data in two situations: density estimation, when the distribution is a mixture of\r\nparametric densities with a nonparametric mixing measure, and accelerated failure time (AFT)\r\nregression modelling, when the same type of mixture is used for the distribution of the error\r\nterm. The Dirichlet process is a popular choice for the mixing measure, yielding a Dirichlet\r\nprocess mixture model for the error; as an alternative, we also allow the mixing measure to be\r\nequal to a normalized inverse-Gaussian prior, built from normalized inverse-Gaussian finite\r\ndimensional distributions, as recently proposed in the literature. Markov chain Monte Carlo\r\ntechniques will be used to estimate the predictive distribution of the survival time, along with\r\nthe posterior distribution of the regression parameters. A comparison between the two models\r\nwill be carried out on the grounds of their predictive power and their ability to identify the\r\nnumber of components in a given mixture density.