Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully Bayesian approach in order to overcome these issues. Posterior inference is carried out by constructing a Metropolis-coupled Markov chain Monte Carlo (MCMC) sampler, which combines Gibbs sampling for the latent cure indicators and Metropolis-Hastings steps with Langevin diffusion dynamics for parameter updates. The main MCMC algorithm is embedded within a parallel tempering scheme by considering heated versions of the target posterior distribution. It is demonstrated via simulations that the proposed algorithm freely explores the multimodal posterior distribution and produces robust point estimates, while it outperforms maximum likelihood estimation via the Expectation-Maximization algorithm. A by-product of our Bayesian implementation is to control the False Discovery Rate when classifying items as cured or not. Finally, the proposed method is illustrated in a real dataset which refers to recidivism for offenders released from prison; the event of interest is whether the offender was re-incarcerated after probation or not.

翻译：事件历史数据中一般治愈模型族的参数估计始终是一项具有挑战性的任务，主要源于似然函数的平坦性和多模态特性。为克服这些问题，本文提出一种全贝叶斯方法。后验推断通过构建耦合马尔可夫链蒙特卡洛（MCMC）采样器实现，该采样器结合了潜在治愈指示变量的吉布斯采样与基于朗之万扩散动力学的参数更新Metropolis-Hastings步骤。主MCMC算法嵌入并行回火方案中，通过考虑目标后验分布的加热版本执行。仿真实验表明，所提算法能自由探索多模态后验分布并生成稳健的点估计，同时优于基于期望最大化算法的最大似然估计。贝叶斯实现的一个副产品是在将个体分类为治愈或未治愈时能够控制错误发现率。最后，将该方法应用于监狱释放人员再犯率的真实数据集，其中感兴趣的事件是罪犯缓刑后是否再次入狱。