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Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…

We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramer-von…

Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…

Many biomolecules have flexible structures, requiring distributional estimates of their conformations. Experiments to acquire distributional data typically measure pairs of labels separately, losing information on the joint distribution.…

For many applications one wishes to decide whether a certain set of numbers originates from an equiprobability distribution or whether they are unequally distributed. Distributions of relative frequencies may deviate significantly from the…

Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…

We study how to combine p-values and e-values, and design multiple testing procedures where both p-values and e-values are available for every hypothesis. Our results provide a new perspective on multiple testing with data-driven weights:…

Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using…

Identifying which taxa in our microbiota are associated with traits of interest is important for advancing science and health. However, the identification is challenging because the measured vector of taxa counts (by amplicon sequencing) is…

There are many different ways in which change point analysis can be performed, from purely parametric methods to those that are distribution free. The ecp package is designed to perform multiple change point analysis while making as few…

This letter studies measurement partitioning and equivalence in state estimation based on graph-theoretic principles. We show that a set of critical measurements (required to ensure LTI state-space observability) can be further partitioned…

The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…

Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…

The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…

As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several…

Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are…

Surveys are commonly used to facilitate research in epidemiology, health, and the social and behavioral sciences. Often, these surveys are not simple random samples, and respondents are given weights reflecting their probability of…

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the…

In this paper we develop tools for observers to use when analysing nebular spectra for temperatures and metallicities, with two goals: to present a new, simple method to calculate equilibrium electron temperatures for collisionally excited…

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes. A completely randomized design is usually used to randomly assign treatment levels to…