任意连续概率分布族的约束替代数据
Constrained surrogates for arbitrary families of continuous probability distributions
- MOE Key Laboratory of Advanced Micro-Structured Materials, and School of Physical Science and Engineering, Tongji University（同济大学先进微结构材料教育部重点实验室和物理科学与工程学院）
- National Key Laboratory of Autonomous Intelligent Unmanned Systems, MOE Frontiers Science Center for Intelligent Autonomous Systems, Tongji University（同济大学国家自主智能无人系统重点实验室和教育部智能自主系统前沿科学中心）
- School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种通用框架，构造任意连续分布族的约束替代数据，实现无需参数估计的无偏模型检验，并应用于多个复杂系统领域。
AI中文摘要：
由参数化概率分布族描述的实证规律可以影响复杂系统被解释和理解的方式。一个反复出现的问题是确定这些描述在多大程度上得到观测数据的支持，以及它们如何被用于刻画底层系统。在此，我们引入一个通用框架，用于构造能够表示任意连续分布族的约束替代数据。我们通过为统计物理学中的若干典型分布提供显式算法来展示其效用，这些分布包括连续幂律、对数正态、指数和截断高斯分布。这些约束替代数据能够基于任意（具有物理意义的）样本统计量实现无偏估计和准确的模型有效性检验，而无需指定或估计模型参数。我们展示了这些理论优势如何在从丛林火灾规模、文本词汇使用到脑连接组和城市人口等应用中转化为更具信息性和细致性的结论。
英文摘要：
Empirical regularities described by parametrized families of probability distributions can shape how complex systems are interpreted and explained. A recurring problem is to determine the extent to which these descriptions are supported by observations, and how they can be used to characterize the underlying system. Here, we introduce a general framework for constructing constrained surrogates capable of representing arbitrary families of continuous distributions. We demonstrate its utility by providing explicit algorithms for several canonical distributions in statistical physics, including continuous powerlaw, lognormal, exponential, and truncated Gaussian distributions. These constrained surrogates enable unbiased estimation and accurate tests of model validity based on arbitrary (physically meaningful) sample statistics, without requiring specification or estimation of model parameters. We show how these theoretical advantages translate into more informative and nuanced conclusions in applications ranging from bushfire magnitudes and word usage in texts to brain connectomes and city populations.
