Related papers: Stein's method for discrete Gibbs measures
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
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…
By a method inspired of the Stein's method, we derive an upper-bound of the Rubinstein distance between two absolutely continuous probability measures on configurations space. As an application, we show that the best way to approximate a…
Stein's method has been widely used to achieve distributional approximations for probability distributions defined in Euclidean spaces. Recently, techniques to extend Stein's method to manifold-valued random variables with distributions…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be…
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…
We apply the Stein-Chen method to problems from extreme value theory. On the one hand, the Stein-Chen method for Poisson approximation allows us to obtain bounds on the Kolmogorov distance between the law of the maximum of i.i.d. random…
Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…
We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we obtain a characterizing non-local Stein operator which boils…
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,…
Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we…
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…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…
This paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment…
We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…
Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…
We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…