Bayesian Nonparametric Survival Analysis using mixture of Burr XII distributions

Abstract: Recently, the Bayesian nonparametric approach in survival studies attracts much more attentions. Because of multi modality in survival data, the mixture models are very common in this field. One of the famous priors on Bayesian nonparametric models is Dirichlet process prior. In this paper we introduce a Bayesian nonparametric mixture model with Burr distribution(Burr type XII) as the kernel of mixture model. Since the Burr distribution shares good properties of common distributions on survival analysis, it has more flexibility than other distributions. By applying this model to simulated and real failure time data sets, we show the preference of this model and compare it with other Dirichlet process mixture models with different kernels. And also we show that this model can be applied for the right censored data. For calculating the posterior of the parameters for inference and modeling, we used the MCMC simulation methods, especially Gibbs sampling.