Related papers: Method of Moments Histograms
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
We introduce Hoop Diagrams, a new visualization technique for set data. Hoop Diagrams are a circular visualization with hoops representing sets and sectors representing set intersections. We present an interactive tool for drawing Hoop…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
Analytical and numerical procedures are applied to show that both third and second order dispersion maps can be explicitly constructed and their mutual effects on the optical pulse propagation are analysed. In these connection it is also…
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using tools from representation theory, Gaetz and Ryba…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally/antinormally ordered moments of photon creation and annihilation operators. Extraction of these…
The modern form of the Moments Method applied to the calculation of the nuclear shell-model level density is explained and examples of the method at work are given. The calculated level density practically exactly coincides with the result…
Two-phase design can reduce the cost of epidemiological studies by limiting the ascertainment of expensive covariates or/and exposures to an efficiently selected subset (phase-II) of a larger (phase-I) study. Efficient analysis of the…
The points of a moment variety are the vectors of all moments up to some order of a family of probability distributions. We study this variety for mixtures of Gaussians. Following up on Pearson's classical work from 1894, we apply current…
In crowded scenes, detection and localization of abnormal behaviors is challenging in that high-density people make object segmentation and tracking extremely difficult. We associate the optical flows of multiple frames to capture…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…
Models phrased though moment conditions are central to much of modern inference. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the…
In this paper, we use tools of information geometry to compare, average and classify histograms. Beta distributions are fitted to the histograms and the corresponding Fisher information geometry is used for comparison. We show that this…
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.…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
This paper proposes a simple unified inference approach on moment restrictions in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters and…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…