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On Stein's method and perturbations [PDF]
ALEA-Latin American Journal of Probability and Mathematical Statistics, 2007 34 ...
Andrew D. Barbour +2 more
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Stein's method and stochastic orderings [PDF]
Advances in Applied Probability, 2009 A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more generals-convex orders are discussed. Attention is focused on Poisson and translated Poisson approximations of a sum of dependent Bernoulli random variables, for example,k-runs
Fraser Daly +2 more
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The Stein-Dirichlet-Malliavin method [PDF]
ESAIM: Proceedings and Surveys, 2015 The Stein’s method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used ...
Decreusefond L.
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Stein's method for diffusion approximations [PDF]
Probability Theory and Related Fields, 1990 Stein's method of obtaining distributional approximations is developed in the context of functional approximation by the Wiener process and other Gaussian processes. An appropriate analogue of the one-dimensional Stein equation is derived, and the necessary properties of its solutions are established.
A. D. Barbour
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Stein's method for rough paths [PDF]
Potential Analysis, 2017 The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use the Stein-Dirichlet method to precise the rate of this convergence in the topology of fractional Sobolev spaces.
Laure Coutin, Laurent Decreusefond
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Self-supervised MRI denoising: leveraging Stein’s unbiased risk estimator and spatially resolved noise maps [PDF]
Scientific Reports, 2023 Thermal noise caused by the imaged object is an intrinsic limitation in magnetic resonance imaging (MRI), resulting in an impaired clinical value of the acquisitions.
Laura Pfaff +8 more
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Automated Parameter Selection for Accelerated MRI Reconstruction via Low-Rank Modeling of Local k-Space Neighborhoods [PDF]
Zeitschrift für Medizinische Physik, 2023 Purpose: Image quality in accelerated MRI rests on careful selection of various reconstruction parameters. A common yet tedious and error-prone practice is to hand-tune each parameter to attain visually appealing reconstructions.
Efe Ilicak +2 more
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Orthogonal Polynomials in Stein's Method [PDF]
Journal of Mathematical Analysis and Applications, 2001 The paper systematically develops a relationship between the classical families of orthogonal polynomials and Stein's method as applied to the distributions in the Pearson and Ord families, that was also discussed by \textit{P. Diaconis} and \textit{S. Zabell} [Stat. Sci. 6, No. 3, 284-302 (1991)].
Wim Schoutens
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Stein's Method and Birth-Death Processes [PDF]
The Annals of Probability, 2001 The representation of a distribution \(Q\) on \(\mathbb{Z}_+\) as the equilibrium distribution of a birth and death process allows a particular realization of Stein's method for \(Q\). The probabilistic argument of \textit{A. Xia} [J. Appl. Probab. 36, No. 1, 287-290 (1999; Zbl 0942.60006)] is extended to yield bounds for the resulting `Stein factors':
Timothy C. Brown, Aihua Xia
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On Stein factors in Stein's method for normal approximation [PDF]
Statistics & Probability LettersBuilding on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the standard normal Stein equation when the test functions belong to the class of real-valued functions whose $k$-th order ...
Robert E. Gaunt
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