Related papers: Size bias for one and all
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…
Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…
In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…
A method is presented to construct goodness-of-fit statistics in many dimensions for which the distribution of all possible test results in the limit of an infinite number of data becomes Gaussian if also the number of dimensions becomes…
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected…
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 general s-convex orders are discussed. Attention is focused on…
We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and…
Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is…
The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the "usual estimator", may be suboptimal in high dimensions. The development of…
Power and sample size analysis comprises a critical component of clinical trial study design. There is an extensive collection of methods addressing this problem from diverse perspectives. The Bayesian paradigm, in particular, has attracted…
The well known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time…
From a macroscopic viewpoint phase transitions as surface melting or growth mode can be described in term of Gibbs excess quantity duly amended by size effect. The aim of this study is to consider such amended quantities to describe surface…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
The size of pretrained models is increasing, and so is their performance on a variety of NLP tasks. However, as their memorization capacity grows, they might pick up more social biases. In this work, we examine the connection between model…
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…
The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect…
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…
We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…
The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation…
In the current paradigm there is a non-trivial bias expected in the process of galaxy formation. Thus, the observed statistical properties of the galaxy distribution do not necessarily extend to the underlying matter distribution.…