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This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…

Probability · Mathematics 2025-09-23 Morgane Austern , Lester Mackey

This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it…

Probability · Mathematics 2021-04-20 Louis H. Y. Chen

Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…

Machine Learning · Statistics 2026-02-02 Tiangang Cui , Shuigen Liu , Xin T. Tong

We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…

Mathematical Physics · Physics 2025-05-28 Razvan Gabriel Iagar , David Puertas-Centeno

In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…

Functional Analysis · Mathematics 2024-11-19 Erlan D. Nursultanov , Durvudkhan Suragan

We detail an approach to develop Stein's method for bounding integral metrics on probability measures defined on a Riemannian manifold $\mathbf M$. Our approach exploits the relationship between the generator of a diffusion on $\mathbf M$…

Probability · Mathematics 2023-04-28 Huiling Le , Alexander Lewis , Karthik Bharath , Christopher Fallaize

Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…

Information Theory · Computer Science 2026-04-28 Mattia Carrino , Stefan Hohenegger

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…

Functional Analysis · Mathematics 2018-12-12 Bastian Hilder , Mark A. Peletier , Upanshu Sharma , Oliver Tse

In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…

Methodology · Statistics 2013-08-21 Min Wang

We provide the first in-depth study of the "smart path" interpolation between an arbitrary probability measure and the gamma-$(\alpha, \lambda)$ distribution. We propose new explicit representation formulae for the ensuing process as well…

Probability · Mathematics 2019-08-20 Benjamin Arras , Yvik Swan

In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…

Probability · Mathematics 2017-10-25 Alberto Chiarini , Alessandra Cipriani , Giovanni Conforti

In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…

Probability · Mathematics 2010-04-06 Gesine Reinert , Adrian Röllin

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

Computation · Statistics 2016-09-05 Shengxin Zhu , Tongxiang Gu , Xiaowen Xu , Zeyao Mo

We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…

Statistics Theory · Mathematics 2024-07-05 Adrian Fischer , Robert E. Gaunt , Yvik Swan

Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…

Machine Learning · Computer Science 2022-12-20 Ibrahim Alsolami , Tomoki Fukai

Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…

Statistics Theory · Mathematics 2015-03-17 Peter Ruckdeschel , Helmut Rieder

The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…

Probability · Mathematics 2016-09-07 Louis H. Y. Chen , Aihua Xia

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

Methodology · Statistics 2022-01-12 Takuo Matsubara , Jeremias Knoblauch , François-Xavier Briol , Chris. J. Oates

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 the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\alpha$-th generalized derivation and ($\alpha$; p)-th weighted Fisher…

Information Theory · Computer Science 2015-10-16 Salimeh Yasaei Sekeh