Statistical Analysis Using Density Surrogates

University Of Washington, Seattle WA

Investigators

Abstract

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.