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We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our…

Probability · Mathematics 2009-06-24 Kshitij Khare , Hua Zhou

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

Applications · Statistics 2009-05-05 Ruth Fuentes-Garcia , Ramses H Mena , Stephen G Walker

Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…

Numerical Analysis · Mathematics 2025-02-07 T. Lewis , X. Xue

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…

Probability · Mathematics 2014-07-08 Guenter Last , Mathew D. Penrose , Matthias Schulte , Christoph Thaele

We show how to achieve the notion of "multicalibration" from H\'ebert-Johnson et al. [2018] not just for means, but also for variances and other higher moments. Informally, it means that we can find regression functions which, given a data…

Machine Learning · Computer Science 2020-08-19 Christopher Jung , Changhwa Lee , Mallesh M. Pai , Aaron Roth , Rakesh Vohra

Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…

Probability · Mathematics 2011-06-13 Gérard Ben Arous , Kim Dang

The sectional curvature of a compact Riemannian manifold M can be seen as a random variable on the Grassmann bundle of 2-planes in TM endowed with the Fubini-Study volume density. In this article we calculate the moments of this random…

Differential Geometry · Mathematics 2017-07-21 Gregor Weingart

Detecting and locating changes in highly multivariate data is a major concern in several current statistical applications. In this context, the first contribution of the paper is a novel non-parametric two-sample homogeneity test for…

Statistics Theory · Mathematics 2012-02-13 Alexandre Lung-Yut-Fong , Céline Lévy-Leduc , Olivier Cappé

Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…

Data Structures and Algorithms · Computer Science 2023-04-11 Megan Bernstein , Matthew Fahrbach , Dana Randall

Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…

Probability · Mathematics 2013-02-05 Mathew D. Penrose , Andrew R. Wade

As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our…

Dynamical Systems · Mathematics 2018-09-06 Michael Baake , Timo Spindeler , Nicolae Strungaru

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…

Computation · Statistics 2026-05-19 Cameron A. Stewart , Maneesh Sahani

We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…

Mathematical Physics · Physics 2015-06-05 Michel Bauer , Tristan Benoist , Denis Bernard

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

Computation · Statistics 2018-07-12 Matthias C. M. Troffaes

The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…

Probability · Mathematics 2024-10-16 Robert C. Griffiths , Matteo Ruggiero , Dario Spanò , Youzhou Zhou

We investigate certain positive random variables having moments of Gamma type. Some necessary and some sufficient conditions are given for their existence. In particular, we observe that the Weber-Schafheitlin formula for the Bessel…

Probability · Mathematics 2023-06-08 Tetyana Kadankova , Thomas Simon , Min Wang

Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…

Methodology · Statistics 2013-07-31 Michael K. Pitt , Minh-Ngoc Tran , Marcel Scharth , Robert Kohn

We study the homogenization of the equation $-A(\frac{\cdot}{\varepsilon}):D^2 u_{\varepsilon} = f$ posed in a bounded convex domain $\Omega\subset \mathbb{R}^n$ subject to a Dirichlet boundary condition and the numerical approximation of…

Numerical Analysis · Mathematics 2024-03-04 Timo Sprekeler

The sample range of uniform random points $X_1, \dots , X_n$ chosen in a given convex set is the convex hull ${\rm conv}[X_1, \dots, X_n]$. It is shown that in dimension three the expected volume of the sample range is not monotone with…

Probability · Mathematics 2016-12-07 Stefan Kunis , Benjamin Reichenwallner , Matthias Reitzner

We prove a characterization of the Dirichlet-Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.

Probability · Mathematics 2023-06-01 Lorenzo Dello Schiavo , Eugene W. Lytvynov