Testing to distinguish measures on metric spaces

02/04/2018

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by   Andrew J. Blumberg, et al.

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We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces ( X, d, μ_1) and ( X, d, μ_2), we are interested in the problem of determining from finite data whether or not μ_1 is μ_2. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogorov--Smirnov test. A real analysis using phylogenetic trees and flu data is presented.