Tolerance intervals provide bounds that contain a specified proportion of a population with a given confidence level, yet their construction remains challenging when parametric assumptions fail or sample sizes are small. Traditional nonparametric methods, such as Wilks' intervals, lack flexibility and often require large samples to be valid. We propose a fully nonparametric approach for constructing one-sided and two-sided tolerance intervals using a calibrated Gibbs posterior. Leveraging the connection between tolerance limits and population quantiles, we employ a Gibbs posterior based on the asymmetric Laplace (check) loss function. A key feature of our method is the calibration of the learning rate, which ensures nominal frequentist coverage across diverse distributional shapes. Simulation studies show that the proposed approach often yields shorter intervals than classical nonparametric benchmarks while maintaining reliable coverage. The framework's practical utility is illustrated through applications in ecology, biopharmaceutical manufacturing, and environmental monitoring, demonstrating its flexibility and robustness across diverse applications.

翻译：容忍区间以给定置信水平提供包含总体特定比例的边界，但当参数假设失效或样本量较小时，其构建仍具挑战性。传统非参数方法（如Wilks区间）缺乏灵活性，且通常需要大样本才能有效。本文提出一种基于校准吉布斯后验的完全非参数方法，用于构建单侧与双侧容忍区间。通过利用容忍限与总体分位数之间的关联，我们采用基于非对称拉普拉斯（勾选）损失函数的吉布斯后验。该方法的关键特征在于学习率的校准，确保在不同分布形态下实现名义频率主义覆盖。仿真研究表明，所提方法在保持可靠覆盖的同时，通常能产生比经典非参数基准更短的区间。通过生态学、生物制药生产和环境监测等领域的应用案例，展示了该框架在实际应用中的灵活性与鲁棒性。