In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds to a percentile bootstrap method of which we give two versions. It is shown that a (non-percentile) smoothed bootstrap method has better behavior and does not need correction for over- or undercoverage. The proofs use martingale methods.

翻译：在近期论文[5]中，作者提出了一种基于可信区间的贝叶斯方法，用于构建单调回归问题中的置信区间。我们从频率学派角度审视该方法，发现其对应一种百分位自助法，并给出了该方法的两个版本。研究表明，（非百分位）平滑自助法具有更优的表现，且无需对过度覆盖或覆盖不足进行修正。相关证明采用了鞅方法。