事件史数据的贝叶斯推断与治愈率建模
Bayesian inference and cure rate modeling for event history data
AI总结：
针对治愈率模型似然函数平坦多峰导致参数估计困难的问题，提出结合Gibbs采样、朗之万Metropolis-Hastings步与并行退火的贝叶斯MCMC方法，仿真与真实再犯数据集验证其性能更优且可控制错误发现率。
摘要：
估计广义治愈率模型族的模型参数一直是一项具有挑战性的任务，主要原因在于似然函数的平坦性与多峰性。本研究提出一种全贝叶斯方法以解决这些问题。后验推断通过构建Metropolis耦合马尔可夫链蒙特卡洛（MCMC）采样器实现，该采样器结合了针对潜在治愈指示变量的Gibbs采样，以及采用朗之万扩散动力学的Metropolis-Hastings步骤进行参数更新。核心MCMC算法通过引入目标后验分布的加热版本，嵌入到并行退火方案中。仿真实验表明，所提算法能够自由探索多峰后验分布并生成稳健的点估计，其性能优于基于期望最大化算法的最大似然估计。本次贝叶斯实现的一个附带作用是在对样本是否治愈进行分类时，能够控制错误发现率。最后，研究在一个关于刑满释放人员再犯情况的真实数据集上对所提方法进行了验证，关注的事件为罪犯在缓刑后是否会被重新监禁。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
