度量空间上区分测度的检验
Testing to distinguish measures on metric spaces
摘要：
我们研究度量空间上两个分布的区分问题;即，给定度量测度空间$({\mathbb X}, d, μ_1)$和$({\mathbb X}, d, μ_2)$，我们感兴趣的是从有限数据确定$μ_1$是否是$μ_2$的问题。关键是使用观测值之间的成对距离，并采用Gromov的重建定理，我们可以使用两个样本Kolmogorov-Smirnov检验来执行这样的检验。一个真正的分析使用系统发育树和流感数据。
英文摘要：
We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces $({\mathbb X}, d, μ_1)$ and $({\mathbb X}, d, μ_2)$, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
