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We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…

Probability · Mathematics 2013-04-18 Kaspar Stucki , Dominic Schuhmacher

We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics…

Probability · Mathematics 2018-12-07 Max Fathi

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We…

Probability · Mathematics 2018-09-28 Robert E. Gaunt , Guillaume Mijoule , Yvik Swan

We use Stein's method to obtain explicit bounds on the rate of convergence for the Laplace approximation of two different sums of independent random variables; one being a random sum of mean zero random variables and the other being a…

Probability · Mathematics 2021-06-29 Robert E. Gaunt

Based on Stein's method, we derive upper bounds for Poisson process approximation in the $L_1$-Wasserstein metric $d_2^{(p)}$, which is based on a slightly adapted $L_p$-Wasserstein metric between point measures. For the case $p=1$, this…

Probability · Mathematics 2009-06-12 Dominic Schuhmacher

We investigate stability of invariant measures of diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to…

Probability · Mathematics 2020-10-28 Max Fathi , Dan Mikulincer

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…

Probability · Mathematics 2015-05-29 Xiao Fang , David Siegmund

Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…

Probability · Mathematics 2018-07-30 Laure Coutin , Laurent Decreusefond

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Probability · Mathematics 2023-04-27 Guillaume Mijoule , Martin Raič , Gesine Reinert , Yvik Swan

In this article we derive quantitative uniqueness and approximation properties for (perturbations) of Riesz transforms. Seeking to provide robust arguments, we adopt a PDE point of view and realize our operators as harmonic extensions,…

Analysis of PDEs · Mathematics 2017-08-16 Angkana Rüland

Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction…

Probability · Mathematics 2021-05-31 Ian W. McKeague , Yvik Swan

Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…

Probability · Mathematics 2024-02-15 A. D. Barbour , Nathan Ross , Guangqu Zheng

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a…

Probability · Mathematics 2018-07-09 Laurent Decreusefond , Aurélien Vasseur

For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…

Numerical Analysis · Mathematics 2019-10-22 Hendrik Ranocha

We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen…

Machine Learning · Statistics 2024-12-02 Nikolas Nüsken

A sampling-based method is introduced to approximate the Gittins index for a general family of alternative bandit processes. The approximation consists of a truncation of the optimization horizon and support for the immediate rewards, an…

Optimization and Control · Mathematics 2023-07-24 Stef Baas , Richard J. Boucherie , Aleida Braaksma

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…

Statistics Theory · Mathematics 2010-02-26 Minjung Kyung , Jeff Gill , George Casella

We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of…

Dynamical Systems · Mathematics 2025-11-05 Juho Leppänen , Yuto Nakajima , Yushi Nakano

Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…

Probability · Mathematics 2018-08-16 Xiao Fang , Qi-Man Shao , Lihu Xu

Performance guarantees for compression in nonlinear models under non-Gaussian observations can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the…

Statistics Theory · Mathematics 2017-10-03 Larry Goldstein , Xiaohan Wei