English
Related papers

Related papers: Approximation of Smooth Numbers for Harmonic Sampl…

200 papers

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

This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…

Numerical Analysis · Mathematics 2026-03-10 Hung D. Nguyen , Thoa Thieu , Liet Vo

Starting from the probability distribution of finite N-body systems, which maximises the Havrda--Charv\'at entropy, we build a Stein-type goodness-of-fit test. The Maxwell--Boltzmann distribution is exact only in the thermodynamic limit,…

Mathematical Physics · Physics 2026-02-16 Jae Wan Shim

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

We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…

Probability · Mathematics 2015-11-19 Enkelejd Hashorva , Mikhail Lifshits , Oleg Seleznjev

In this paper, the Milstein method is used to approximate invariant measures of stochastic differential equations with commutative noise. The decay rate of the transition probability kernel generated by the Milstein method to the unique…

Numerical Analysis · Mathematics 2019-01-28 Lihui Weng , Wei Liu

We explore two aspects of geometric approximation via a coupling approach to Stein's method. Firstly, we refine precision and increase scope for applications by convoluting the approximating geometric distribution with a simple translation…

Probability · Mathematics 2024-12-11 Fraser Daly , Claude Lefèvre

We obtain Stein approximation bounds for stochastic integrals with respect to a Poisson random measure over ${\Bbb R}^d$, $d\geq 2$. This approach relies on third cumulant Edgeworth-type expansions based on derivation operators defined by…

Probability · Mathematics 2018-06-04 Nicolas Privault

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…

Probability · Mathematics 2016-03-28 Christophe Ley , Gesine Reinert , Yvik Swan

This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…

Statistics Theory · Mathematics 2026-01-19 Robert E. Gaunt , Frédéric Ouimet , Donald Richards

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

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Probability · Mathematics 2024-11-06 Dominic Schuhmacher , Leoni Carla Wirth

We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…

Numerical Analysis · Mathematics 2024-05-17 Andrea Bonito , Diane Guignard , Wenyu Lei

We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…

Probability · Mathematics 2019-05-27 Julian Fischer

Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the…

Probability · Mathematics 2024-12-10 Robert E. Gaunt

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…

Machine Learning · Computer Science 2017-05-24 H. -Ch. Ruiz , H. J. Kappen

We use Stein's method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of marked Poisson point processes on $\mathbb{R}^d$. As in the study under the weaker…

Probability · Mathematics 2020-11-17 Tianshu Cong , Aihua Xia

Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…

Statistics Theory · Mathematics 2017-12-29 Chris J. Oates , Jon Cockayne , François-Xavier Briol , Mark Girolami

Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…

Methodology · Statistics 2015-06-23 Zhong Guan

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the…

Econometrics · Economics 2020-03-02 Dennis Kristensen , Patrick K. Mogensen , Jong Myun Moon , Bertel Schjerning