ﻻ يوجد ملخص باللغة العربية
Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two distributions differ. Given samples from two densities $f_1$ and $f_0$, we consider the task of localizing occurrences of the inequality $f_1 > f_0$. To avoid the challenges associated with high-dimensional space, we propose a general hypothesis testing framework where hypotheses are formulated adaptively to the data by conditioning on the combined sample from the two densities. We then investigate a special case of this framework where the notion of locality is captured by a random walk on a weighted graph constructed over this combined sample. We derive a tractable testing procedure for this case employing a type of scan statistic, and provide non-asymptotic lower bounds on the power and accuracy of our test to detect whether $f_1>f_0$ in a local sense. Furthermore, we characterize the tests consistency according to a certain problem-hardness parameter, and show that our test achieves the minimax detection rate for this parameter. We conduct numerical experiments to validate our method, and demonstrate our approach on two real-world applications: detecting and localizing arsenic well contamination across the United States, and analyzing two-sample single-cell RNA sequencing data from melanoma patients.
This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and symmetric Lapla
This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio property. Included in this class of distributions are the Students t, the Pareto, and many other distributions. W
A scoring rule is a loss function measuring the quality of a quoted probability distribution $Q$ for a random variable $X$, in the light of the realized outcome $x$ of $X$; it is proper if the expected score, under any distribution $P$ for $X$, is mi
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlat
We discuss a general approach to handling multiple hypotheses testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypot