Robust Bayesian methods for survival analysis using rate mixtures of Weibull distributions
Catalina Vallejos, University of Warwick
Venue: Room A54, Postgraduate Statistics Centre, Lancaster University
Date: 24-10-2013, 4pm
Survival models such as the Weibull or log-normal lead to inference that is not robust to the presence of outliers. They also assume that all heterogeneity between individuals can be modelled through covariates. This article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues. This can be interpreted as the introduction of a random effect in the survival distribution. We introduce the family of Rate Mixtures of Weibull distributions, which includes the known Lomax distribution. Bayesian inference under a prior that combines the structure of the Jeffreys' prior and a proper (informative) prior is implemented and the existence of the posterior distribution is verified. In addition, a method for outlier detection based on the mixture structure is proposed. Finally, the analysis is illustrated using real datasets.