Related papers: Stein's Method for Probability Distributions on $\…
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…
Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…
The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will…
We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…
We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to create a cavity. Another advantage is that it gives limit…
We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence using Stein's method. For the non-degenerate case, our results extend recent…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
The purpose of this paper is to analyze the distribution distance between random vectors derived from the magnitude of the analytic wavelet transform of the squared envelopes of Gaussian processes and their large-scale limits. When the…
We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting…
We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
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…