Related papers: An Urn Model of Diaconis

The Kneser-Poulsen conjecture says that if a finite collection of balls in a d-dimensional Euclidean space is rearranged so that the distance between each pair of centers does not get smaller, then the volume of the union of these balls…

We study how measures with finite lower density are distributed around $(n-m)$-planes in small balls in $\mathbb{R}^n$. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large…

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…

From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…

We introduce a modification of the generalized P\'olya urn model containing two urns and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$, $J\in\mathbb{N}$ added to the urns after $n$ draws. We provide sufficient…

Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…

Since its inception in 1907, the Ehrenfest urn model (EUM) has served as a test bed of key concepts of statistical mechanics. Here we employ this model to study large deviations of a time-additive quantity. We consider two continuous-time…

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system.…

We use death processes and embeddings into continuous time in order to analyze several urn models with a diminishing content. In particular we discuss generalizations of the pill's problem, originally introduced by Knuth and McCarthy, and…

This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…

Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…

In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters can support multiple parties by…

In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.

A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference…

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…

We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.