A Bayesian semiparametric accelerate failure time mixture cure model

The accelerated failure time mixture cure (AFTMC) model is widely used for survival data when a portion of patients can be cured. In this paper, a Bayesian semiparametric method is proposed to obtain the estimation of parameters and density distribution for both the cure probability and the survival distribution of the uncured patients in the AFTMC model. Specifically, the baseline error distribution of the uncured patients is nonparametrically modeled by a mixture of Dirichlet process. Based on the stick-breaking formulation of the Dirichlet process, the techniques of retrospective and slice sampling, an efficient and easy-to-implement Gibbs sampler is developed for the posterior calculation. The proposed approach can be easily implemented in commonly used statistical softwares, and its performance is comparable to fully parametric method via comprehensive simulation studies. Besides, the proposed approach is adopted to the analysis of a colorectal cancer clinical trial data.

A two-stage Bayesian semiparametric model for novelty detection with robust prior information

Novelty detection methods aim at partitioning the test units into already observed and previously unseen patterns. However, two significant issues arise: there may be considerable interest in identifying specific structures within the novelty, and contamination in the known classes could completely blur the actual separation between manifest and new groups. Motivated by these problems, we propose a two-stage Bayesian semiparametric novelty detector, building upon prior information robustly extracted from a set of complete learning units. We devise a general-purpose multivariate methodology that we also extend to handle functional data objects. We provide insights on the model behavior by investigating the theoretical properties of the associated semiparametric prior. From the computational point of view we, propose, a suitable $$\varvec{\xi }$$ ξ : $$\varvec{\xi }$$ ξ -sequence to construct an independent slice-efficient sampler that takes into account the difference between manifest and novelty components. We showcase our model performance through an extensive simulation study and applications on both multivariate and functional datasets, in which diverse and distinctive unknown patterns are discovered.