Bayesian paradigm takes advantage of well-fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through a Bayesian analysis of survival modeling for multivariate survival outcomes with the complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of the ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis, and Stan relaxes the posterior inference.

Partially missing data sets are a prevailing problem in pattern recognition. In this paper, the problem of clustering incomplete data sets is considered, and missing attribute values are imputed by the centers of corresponding nearest-neighbor intervals. Firstly, the algorithm estimates the nearest-neighbor intervals of missing attribute values by using the attribute distribution information of the data sets sufficiently. Secondly, the missing attribute values are imputed by the center of the intervals so as to clustering incomplete data sets. The proposed algorithm introduces the nearest neighbor information into incomplete data clustering, and the comparisons of the experimental results for two UCI data sets demonstrate the capability of the proposed algorithm.

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