Statistical Analysis Using Density Surrogates

密度替代值是可以帮助测量看到具有某些特征的观测的可能性的量。该项目旨在开发基于密度替代的新的统计方法，并分析潜在的理论特性。该项目开发的方法将应用于解决科学问题，例如使用GPS数据调查人类活动和检测宇宙内部的物质分布。该项目的重点是开发新的统计方法，用于使用密度代理分析复杂数据集。密度替代项是类似于概率密度的数量，它表征了观察到的随机样本的潜在分布。密度代理的例子包括层次聚类中的连锁标准、k最近邻域的半径和核密度估计的期望值。本计画提出数种新颖的密度替代物，并设计新的统计工具。这些新的密度替代物可用于在传统的基于密度的方法失败的情况下进行统计分析。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Density surrogates are quantities that can help measure the likelihood of seeing observations with certain characteristics. This project aims at developing novel statistical approaches based on density surrogates and analyzing the underlying theoretical properties. Methodologies developed from this project will be applied to solving scientific questions such as investigating human activities using GPS data and detecting matter distribution inside our Universe.This project focuses on developing new statistical methodologies for analyzing complex data sets using density surrogates. Density surrogates are quantities similar to the probability density that characterizes the underlying distribution of the observed random sample. Examples of density surrogates include the linkage criterion in a hierarchical clustering, radius of the k-nearest neighborhood, and expected value of a kernel density estimator. This project proposes several novel density surrogates and designs new statistical tools. These new density surrogates can be used to perform statistical analysis in situations where the conventional density-based approaches fail.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.