发表机构
Bocconi University; University of Milano-Bicocca; University of Torino（博科尼大学; 米兰比可卡大学; 都灵大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对物种和特征抽样中模态缺失概率推断缺乏统一框架且现有方法过于保守的问题，提出基于贝叶斯非参数模型的统一推断框架，生成更尖锐的闭式置信区间，兼顾频率论稳健性，并经模拟和有组织犯罪应用验证。
AI 中文摘要
物种和特征抽样问题在每当每个观测单元与可数字母表中的一个或多个标签相关联时自然出现，推断关注的是该字母表上分布中未观测到的部分。在此框架内，最近的贡献已将注意力从对未见标签总概率质量的推断转向对最大未见标签概率（即模态缺失概率）的无分布置信区间，从而提供更精细的信息，说明缺失质量是集中在少数高流行率的未见标签上，还是分布在许多可忽略的标签上。除了缺乏物种和特征的统一框架外，这些方法采用最坏情况视角，导致大量信息损失并产生过于保守的区间。我们通过一个统一的基于模型的框架来解决这些局限性，用于在物种和特征设置中对模态缺失概率进行推断，该框架利用灵活的贝叶斯非参数公式将与观测数据兼容的模型周围的不确定性局部化。这导致更尖锐的闭式置信区间，有效利用先验信息和观测数据，同时保留无分布区间的理论频率论性质和稳健性。模拟研究证实了这些改进，而一个有组织犯罪应用说明了我们的贡献如何有可能重塑调查中的执法决策。
英文摘要
Species and feature sampling problems arise naturally whenever each observed unit is associated with one or more labels from a countable alphabet, and inference focuses on the unobserved portion of the distribution over such an alphabet. Within this framework, recent contributions have shifted attention from inference on the total probability mass over unseen labels to distribution-free confidence intervals for the largest unobserved label probability (i.e., the modal missing probability), thereby providing more refined information on whether the missing mass is concentrated on a few high-prevalence unseen labels or distributed across many negligible ones. Besides lacking a unified framework for species and features, these approaches employ a worst-case perspective that causes substantial information loss and produces overly-conservative intervals. We address these limitations through a unified model-based framework for inference on modal missing probabilities in both species and feature settings, which leverages a flexible Bayesian nonparametric formulation to localize uncertainty around models compatible with the observed data. This leads to sharper closed-form credible intervals that effectively exploit prior information and observed data, while preserving the theoretical frequentist properties and robustness of distribution-free intervals. Simulation studies confirm these improvements, while an organized crime application illustrates how our contribution has the potential to reshape law-enforcement decision-making in investigations.
