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We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation…

Probability · Mathematics 2024-09-04 Bero Roos

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…

Machine Learning · Statistics 2026-05-20 Thiago R. Ramos , Helton Graziadei , Luben M. C. Cabezas

We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…

Probability · Mathematics 2013-03-21 Erol A. Peköz , Adrian Röllin , Nathan Ross

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

Probability · Mathematics 2018-05-04 Carina Betken , Hanna Döring , Marcel Ortgiese

In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to…

Probability · Mathematics 2022-10-14 Partha S. Dey , Grigory Terlov

This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its…

Numerical Analysis · Mathematics 2024-10-17 Nicolae Suciu , Surendra Nepal , Yosief Wondmagegne , Magnus Ögren , Adrian Muntean

We consider $M/Ph/n+M$ queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein-Uhlenbeck (OU) process is bounded by…

Probability · Mathematics 2015-12-01 Anton Braverman , J. G. Dai

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

Statistics Theory · Mathematics 2018-10-03 Jonathan H. Huggins , Trevor Campbell , Mikołaj Kasprzak , Tamara Broderick

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

Probability · Mathematics 2013-04-05 Christophe Ley , Yvik Swan

We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…

Methodology · Statistics 2019-09-10 Zdravko I. Botev , Pierre L'Ecuyer

We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…

Probability · Mathematics 2025-04-14 Chiara Amorino , Arturo Jaramillo , Mark Podolskij

Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…

Probability · Mathematics 2022-06-02 Jiaqi Xi , Jonathan Niles-Weed

Motivated by its appearance as a limiting distribution for random and non-random sums of independent random variables, in this paper we develop Stein's method for approximation by the asymmetric Laplace distribution. Our results generalise…

Probability · Mathematics 2026-05-15 Fraser Daly , Robert E. Gaunt , Heather L. Sutcliffe

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

Probability · Mathematics 2022-09-21 Robert E. Gaunt , Heather Sutcliffe

We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…

Statistics Theory · Mathematics 2023-02-03 Clément Dombry , Thibault Modeste , Romain Pic

Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein's method, one needs to establish a Stein…

Probability · Mathematics 2007-05-23 Andrew D. Barbour , Vydas Cekanavicius , Aihua Xia

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…

Probability · Mathematics 2014-09-15 Dominic Schuhmacher , Kaspar Stucki

In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…

Probability · Mathematics 2022-01-06 Kalyan Barman , N. S. Upadhye

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

Probability · Mathematics 2019-04-08 Benjamin Arras , Christian Houdré

The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of…

Information Theory · Computer Science 2013-04-30 Igal Sason