标题： 用离散顺序统计量建模潜在的次泊松分布 显示英文标题

标题： Modeling Latent Underdispersion with Discrete Order Statistics

摘要： 泊松分布是计数数据概率模型的默认似然选择。 然而，由于泊松分布的等方差约束，此类模型可能具有人为膨胀的预测不确定性。 虽然过度离散已被广泛研究，但条件下的不足离散——其中潜在结构使数据比泊松分布更规律——仍研究不足，部分原因是缺乏可处理的建模工具。 我们引入了一类基于离散顺序统计量的新模型，假设观测到的计数是某些离散母分布（如泊松或负二项分布）独立同分布抽样的顺序统计量（例如，最小值、中位数、最大值）。 我们开发了一个通用的数据增强方案，与针对母分布的现有工具模块化，使得在各种此类模型中能够进行参数估计或后验推断。 我们描述了泊松和负二项顺序统计量的特性，揭示了它们离散性的可解释控制参数。 我们将我们的框架应用于四个案例研究——即商业航班时间、新冠病例计数、芬兰鸟类丰富度和RNA测序数据——并展示了所提出框架的灵活性和普遍性。 我们的结果表明，顺序统计量模型可以像常用的替代方法一样构建、使用和解释，同时通常获得更好的拟合，并在计数数据出现的广泛应用领域中展现出前景。 显示英文摘要

摘要： The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated. While overdispersion has been extensively studied, conditional underdispersion -- where latent structure renders data more regular than Poisson -- remains underexplored, in part due to the lack of tractable modeling tools. We introduce a new class of models based on discrete order statistics, where observed counts are assumed to be an order statistic (e.g., minimum, median, maximum) of i.i.d. draws from some discrete parent, such as the Poisson or negative binomial. We develop a general data augmentation scheme that is modular with existing tools tailored to the parent distribution, enabling parameter estimation or posterior inference in a wide range of such models. We characterize properties of Poisson and negative binomial order statistics, exposing interpretable knobs on their dispersion. We apply our framework to four case studies -- i.e., to commercial flight times, COVID-19 case counts, Finnish bird abundance, and RNA sequencing data -- and illustrate the flexibility and generality of the proposed framework. Our results suggest that order statistic models can be built, used, and interpreted in much the same way as commonly-used alternatives, while often obtaining better fit, and offer promise in the wide range of applications in which count data arise.