32 citations · 167 across the 40 of their papers we have counts for
46 papers
Representations of solutions to Stein equations and their derivatives
Ferdinand Rapin, Yvik Swan
We propose pointwise representations of the Stein solution to a weighted first-order Stein equation associated with a univariate absolutely continuous distribution. The representat…
Explicit Gamma-Stein Bounds for Satterthwaite's Approximation
Gabriel Bailly, Ferdinand Rapin, Yvik Swan +1
We derive explicit Gamma--Stein bounds for the Satterthwaite approximation of weighted sums of independent chi-square random variables and, more generally, of independent Gamma ran…
Edgeworth expansion on Wiener chaos
Paul Mansanarez, Guillaume Poly, Yvik Swan
Consider an element of the -th Wiener chaos $\WW_p$, and denote by $\prob_F$ its law. For a positive integer , let be the Radon measure with density…
Stein's method for Fréchet approximation: a regularly varying functions approach
Paul Mansanarez, Guillaume Poly, Yvik Swan
We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our…
Split Conformal Prediction under Data Contamination
Jase Clarkson, Wenkai Xu, Mihai Cucuringu +2
Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable…
Stein's Method of Moments on the Sphere
Adrian Fischer, Robert E. Gaunt, Yvik Swan
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,…
Stein's method of moments for truncated multivariate distributions
Adrian Fischer, Robert E. Gaunt, Yvik Swan
We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asympt…
One-dimensional Stein's method with bespoke derivatives
Gilles Germain, Yvik Swan
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete dist…
Derivatives of entropy and the MMSE conjecture
Paul Mansanarez, Guillaume Poly, Yvik Swan
We investigate the entropy of a probability measure along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided th…
Stein's Method of Moments
Bruno Ebner, Adrian Fischer, Robert E. Gaunt +2
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for margin…
Independent additive weighted bias distributions and associated goodness-of-fit tests
Bruno Ebner, Yvik Swan
We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related -type disc…
Normal approximation for the posterior in exponential families
Adrian Fischer, Robert E. Gaunt, Gesine Reinert +1
In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in expo…
A note on one-dimensional Poincaré inequalities by Stein-type integration
Gilles Germain, Yvik Swan
We study the weighted Poincaré constant of a probability density with weight function using integration methods inspired by Stein's method. We obtain a new version…
Stein's method and approximating the multidimensional quantum harmonic oscillator
Ian W. McKeague, Yvik Swan
Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representat…
Stein's Method Meets Computational Statistics: A Review of Some Recent Developments
Andreas Anastasiou, Alessandro Barp, François-Xavier Briol +11
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…
Stein's density method for multivariate continuous distributions
Guillaume Mijoule, Martin Raič, Gesine Reinert +1
This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonica…
Simple variance bounds with applications to Bayesian posteriors and intractable distributions
Fraser Daly, Fatemeh Ghaderinezhad, Christophe Ley +1
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taki…
Distances between distributions via Stein's method
Marie Ernst, Yvik Swan
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 s…
On infinite covariance expansions
Marie Ernst, Gesine Reinert, Yvik Swan
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead…
First order covariance inequalities via Stein's method
Marie Ernst, Gesine Reinert, Yvik Swan
We propose probabilistic representations for inverse Stein operators (i.e. solutions to Stein equations) under general conditions; in particular we deduce new simple expressions fo…
Some new Stein operators for product distributions
Robert E. Gaunt, Guillaume Mijoule, Yvik Swan
We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent r…
Stein-type covariance identities: Klaassen, Papathanasiou and Olkin-Shepp type bounds for arbitrary target distributions
Marie Ernst, Gesine Reinert, Yvik Swan
In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wi…
Stein operators, kernels and discrepancies for multivariate continuous distributions
Guillaume Mijoule, Gesine Reinert, Yvik Swan
In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which w…
Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem
Thomas Gallouët, Guillaume Mijoule, Yvik Swan
Consider the multivariate Stein equation , where is a standard -dimensional Gaussian random vector, and let be the solution give…