Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a unified theory for posterior distributions in this setting, not requiring the priors to be conjugate. We first derive contraction rate results for wide classes of histogram priors on the unknown hazard function and prove asymptotic normality of linear functionals of the posterior hazard in the form of Bernstein--von Mises theorems. Second, using recently developed multiscale techniques, we derive functional limiting results for the cumulative hazard and survival function. Frequentist coverage properties of Bayesian credible sets are investigated: we prove that certain easily computable credible bands for the survival function are optimal frequentist confidence bands. We conduct simulation studies that confirm these predictions, with an excellent behavior particularly in finite samples, showing that even simplest possible Bayesian credible bands for the survival function can outperform state-of-the-art frequentist bands in terms of coverage.

翻译：Bayesian Cox 比例危害模型通常使用小数常数前程来进行生存分析。 尽管它很受欢迎, 但这种Bayesian 方法的大量样本特性尚未被很好地理解。 这项工作为在这一背景下的后方分布提供了一个统一的理论, 不需要先有交配。 我们首先根据未知危害函数来测测算大量直方图前端的收缩率, 并证明以Bernstein- von Mises 理论为形式的后端危险线性功能无症状常态。 第二, 我们使用最近开发的多尺度技术, 得出累积危害和生存功能的功能限制效果。 调查了Bayesian 可靠组的常态覆盖特性: 我们证明某些容易比较可靠的生存功能频谱是最佳的常态信任带。 我们进行模拟研究, 证实这些预测, 特别在有限的样本中表现了极好的行为, 显示即使最简单的Bayesian 可靠的生存功能频带在覆盖范围上也超越了最先进的常态频带。