Decompounding on compact Lie groups

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference

Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using Compound Poisson Processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.Comment: 23 pages, 8 figures, 21 reference

Infinitely divisible central probability measures on compact Lie groups---regularity, semigroups and transition kernels

We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type measures. We find conditions for such a measure to have a smooth density and give examples. The Hunt semigroup and generator of convolution semigroups of measures are represented as pseudo-differential operators. For sufficiently regular convolution semigroups, the transition kernel has a tractable Fourier expansion and the density at the neutral element may be expressed as the trace of the Hunt semigroup. We compute the short time asymptotics of the density at the neutral element for the Cauchy distribution on the $d$-torus, on SU(2) and on SO(3), where we find markedly different behaviour than is the case for the usual heat kernel.Comment: Published in at http://dx.doi.org/10.1214/10-AOP604 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Density estimation on the rotation group using diffusive wavelets

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an existing technique using the De La Vall\'ee Poussin kernel estimator. The heat-kernel wavelet approach appears to offer the best convergence, with faster convergence to the optimal bound and guaranteed positivity of the estimated probability density function

von Mises-Fisher approximation of multiple scattering process on the hypersphere

International audienceThis paper presents a ''method of moments'' estimation technique for the study of multiple scattering on the hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particules in random media

Maxentropic and quantitative methods in operational risk modeling

In risk management the estimation of the distribution of random sums or collective models from historical data is not a trivial problem. This is due to problems related with scarcity of the data, asymmetries and heavy tails that makes difficult a good fit of the data to the most frequent distributions and existing methods. In this work we prove that the maximum entropy approach has important applications in risk management and Insurance Mathematics for the calculation of the density of aggregated risk events, and even for the calculation of the individual losses that come from the aggregated data, when the available information consists of an observed sample, which we usually do not have any information about the underlying process. From the knowledge of a few fractional moments, the Maxentropic methodologies provide an efficient methodology to determine densities when the data is scarce, or when the data presents correlation, large tails or multimodal characteristics. For this procedure, the input would be the sample moments E[e S] = ( ) or some interval that encloses the di fference between the true value of ( ) and the sample moments (for eight values of the Laplace transform), this interval would be related to the uncertainty (error) in the data, where the width of the interval may be adjusted by convenience. Through a simulation study we analyze the quality of the results, considering the differences with respect to the true density and in some cases the study of the size of the gradient and the time of convergence. We compare four different extensions of Maxentropic methodologies, the Standard Method of Maximum Entropy (SME), an extension of this methodology allows to incorporate additional information through a reference measure, called Method of Entropy in the Mean (MEM) and two extensions of the SME that allow introduce errors, called SME with errors or SMEE. Although our motivating example come from the field of Operational Risk analysis, the developed methodology may be applied to any branch of applied sciences.Programa de Doctorado en Economía de la Empresa y Métodos Cuantitativos por la Universidad Carlos III de MadridPresidente: Alejandro Balbás de la Corte; Secretario: Argimiro Arriata Quesada; Vocal: Santiago Carrillo Menénde

Isotropic Multiple Scattering Processes on Hyperspheres

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres ${\mathbb S}^{p-1}$. It allows one to derive the Fourier expansions on ${\mathbb S}^{p-1}$ of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on ${\mathbb S}^{p-1}$ is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on ${\mathbb S}^{p-1}$ are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on ${\mathbb S}^{p-1}$.Comment: 16 pages, 4 figure

The very model of a modern linguist — in honor of Helge Dyvik

publishedVersio

Term-driven E-Commerce

Die Arbeit nimmt sich der textuellen Dimension des E-Commerce an. Grundlegende Hypothese ist die textuelle Gebundenheit von Information und Transaktion im Bereich des elektronischen Handels. Überall dort, wo Produkte und Dienstleistungen angeboten, nachgefragt, wahrgenommen und bewertet werden, kommen natürlichsprachige Ausdrücke zum Einsatz. Daraus resultiert ist zum einen, wie bedeutsam es ist, die Varianz textueller Beschreibungen im E-Commerce zu erfassen, zum anderen können die umfangreichen textuellen Ressourcen, die bei E-Commerce-Interaktionen anfallen, im Hinblick auf ein besseres Verständnis natürlicher Sprache herangezogen werden

Proceedings of the 17th Annual Conference of the European Association for Machine Translation

Proceedings of the 17th Annual Conference of the European Association for Machine Translation (EAMT