Related papers: Multidimensional Stein's method for Gamma approxim…
In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…
We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
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…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density…
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…
In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to…
In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach,…
We show new estimates for the total variation and Wasserstein distances in the framework of the Breuer-Major theorem. The results are based on the combination of Stein's method for normal approximations and Malliavin calculus together with…
In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
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…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b])=1, define the hierarchical sequence of random variables {X_n}_{n\ge 0} by X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such sequences arise from…
We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
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…