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.
翻译:我们认为右检查生存模型中的巴伊西亚非参数推论是非参数推论,这种推论是按危险率进行模拟的。我们从危险线性功能和“许多”功能的后方限制分布,然后在适当的多尺度空间同时进行“许多”功能。作为一种应用,我们从Bernstein-von Misorem中得出累积危险和生存功能的Bernstein-von Misorems理论,从而导致这些数量无症状地高效的置信带。此外,我们从最高标准的角度显示了危害的最佳后后方收缩率。在医学研究中,流行的方法是将前方危险作为可能依赖高度的随机直方图来模拟。这种以及更一般的任意平稳先前分布类别被认为是我们理论的应用。为可能依赖直方图后方的后方提供了取样器。根据模拟和真实的数据实验对有限的样本特性进行了调查。