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We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…

Probability · Mathematics 2025-08-05 Robert E. Gaunt , Siqi Li , Heather Sutcliffe

We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…

Probability · Mathematics 2024-03-19 Takahiro Hasebe , Alexey Kuznetsov

Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of…

Machine Learning · Statistics 2018-10-30 Qiang Liu , Dilin Wang

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

Statistics Theory · Mathematics 2018-07-19 Zhuoran Yang , Krishnakumar Balasubramanian , Han Liu

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…

Methodology · Statistics 2023-12-25 Simon Nik , Christian H. Weiß

We propose Stein-type estimators for zero-inflated Bell regression models by incorporating information on model parameters. These estimators combine the advantages of unrestricted and restricted estimators. We derive the asymptotic…

Computation · Statistics 2024-03-04 Solmaz Seifollahi , Hossein Bevrani , Zakariya Yahya Algamal

We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\R$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$ is supposed or…

Probability · Mathematics 2012-07-24 Christian Döbler

Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…

Mathematical Physics · Physics 2019-05-01 Jean-Christophe Mourrat

We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…

Probability · Mathematics 2025-10-01 David Grzybowski , Mark Meckes

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

Methodology · Statistics 2026-01-08 Yuanying Chen , Tongyu Li , Yang Bai , Zhenhua Lin

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples…

Machine Learning · Statistics 2021-10-11 Zheyang Shen , Markus Heinonen , Samuel Kaski

In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…

Probability · Mathematics 2020-10-20 Amit N. Kumar

We present systematic construction of probability and probability current densities operators for one-band single particle Pauli equations starting from the operators in Dirac electron model within Second Quantized Approach. These operators…

Mesoscale and Nanoscale Physics · Physics 2017-08-15 E. L. Rumyantsev , P. E. Kunavin

In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein…

Probability · Mathematics 2020-05-05 Amit N. Kumar , Neelesh S. Upadhye , P. Vellaisamy

Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…

The class of $\alpha$-stable distributions with a wide range of applications in economics, telecommunications, biology, applied, and theoretical physics. This is due to the fact that it possesses both the skewness and heavy tails. Since…

Statistics Theory · Mathematics 2018-11-13 Mahdi Teimouri

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…

Probability · Mathematics 2022-03-15 Thomas Bonis

We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…

Probability · Mathematics 2019-11-14 Abdelmalek Abdesselam

Stein variational gradient descent (SVGD) refers to a class of methods for Bayesian inference based on interacting particle systems. In this paper, we consider the originally proposed deterministic dynamics as well as a stochastic variant,…

Machine Learning · Statistics 2021-02-26 Nikolas Nüsken , D. R. Michiel Renger

In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…

Numerical Analysis · Computer Science 2015-12-11 V. N. Petrushin , E. V. Nikulchev , D. A. Korolev