论文标题
多尺度贝叶斯生存分析
Multiscale Bayesian Survival Analysis
论文作者
论文摘要
我们认为在右审查生存模型中贝叶斯非参数推断，在危险率的水平上进行建模。我们得出危险线性功能的后限制分布，然后在适当的多尺度空间中同时使用“许多”功能。作为一种应用，我们为累积危害和生存函数得出了Bernstein-von Mises定理，这导致这些数量的渐近有效的置信带。此外，我们在上皮规范方面显示出危害的最佳后验收率。在医学研究中，一种流行的方法是将危害危险建模为可能依赖高度的随机直方图。这种任意平滑的先验分布的这种和更一般的类别被视为我们理论的应用。为可能的依赖直方图后代提供了采样器。在模拟和实际数据实验上研究了其有限样本属性。
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many' functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein-von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.
