Related papers: The normal distribution in some constrained sample…
Necessary and sufficient conditions for a measure to be an extreme point of the set of measures (on an abstract measurable space) with prescribed generalized moments are given, as well as an application to extremal problems over such moment…
Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is…
In this paper, by using the concept of positive elements of $C^*$-algebras instead of the real numbers $\mathbb{R}$, a generalization of distribution functions, with a particular focus on distance distribution functions has been introduced…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
This note reports on some attempts to examine if and under which conditions the naturally scaled probability measures associated to an orthonormal basis of a classical Paley-Wiener space converge to a uniform distribution (on a compact set…