相关论文: On Stein's method and perturbations

We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…

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…

In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…

This exposition explains the basic ideas of Stein's method for Poisson random variable approximation and Poisson process approximation from the point of view of the immigration-death process and Palm theory. The latter approach also enables…

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

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…

In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…

We study the accuracy of a scaled Poisson approximation to the weighted sum of independent Poisson random variables, focusing on in particular the relative error of the tail distribution. A bound on the relative approximation error is…

In this paper we give a historical account of the development of Poisson approximation using Stein's method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on…

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

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…

Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either…

The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…

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…

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…

Narayana numbers appear in many places in combinatorics and probability, and it is known that they are asymptotically normal. Using Stein's method of exchangeable pairs, we provide an error of approximation in total variation to a symmetric…

The main purpose of the paper is to investigate the possibility of applying Chen-Stein approach to estimate the $\chi^2$ distance between Poisson distribution and a sum of independent indicators. Earlier results concerning $\chi^2$ distance…

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…

We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bound for the approximation error, which is of order 1/N in…