Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices

L2 Boosting on generalized Hoeffding decomposition for dependent variables. Application to Sensitivity Analysis

This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional settings. Then, we apply a greedy algorithm with these previous estimators to Sensitivity Analysis. We also establish the consistency of this $\mathbb L_2$-boosting up to sparsity assumptions on the signal to analyse. We end the paper with numerical experiments, which demonstrates the low computational cost of our method as well as its efficiency on standard benchmark of Sensitivity Analysis.Comment: 48 pages, 7 Figure

Meta-Analysis on grain yield effects of cereals-legume intercropping

Meta-Analysis on grain yield effects of cereals-legume intercroppin

Generalized Sobol sensitivity indices for dependent variables: numerical methods

International audienceThe hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X_1,..., X_p are assumed to be dependent, this decomposition is unique if components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=f(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y with respect to the dependent inputs X. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem

Égypte : grèves de masse, espace public oppositionnel et insurrection des consciences

Le 10 décembre 2011. Une révolution qui continue et s’approfondit, révélatrice de transformations mondiales La révolution égyptienne associe dans un même temps un espace oppositionnel public très largement visible, place Tahrir et internet, un peu moins avec les journaux muraux urbains, une insurrection des consciences qui révise les hiérarchies des valeurs personnelles et bouscule les relations matrimoniales au sein de la famille, et, enfin, des vagues de manifestations et grèves massives, p..

L2-Boosting for sensitivity analysis with dependent inputs

International audienceThis paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional setting. We then apply a greedy algorithm with these previous estimators to a sensitivity analysis. We also establish the consistency of this L2-boosting under sparsity assumptions of the signal to be analyzed. The paper concludes with numerical experiments, that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis

Mécanique statistique de systèmes macroscopiques hors-équilibre

Over the last two decades, formalism in statistical mechanics describing states far from equilibrium has been significantly developed. However, there are few experimental achievements to test exact results and robustness when the system is far from the assumptions under which they are established. On this basis, we propose to consider macroscopic systems that allow good control of experimental parameters. We report here the study of two dissipative systems maintained in a steady state.On the one hand, we study the dynamics of a single bead bouncing vertically upon avibrated surface. We consider the properties of energy exchanges between the particle (bead) and the thermostat (the vibrated surface) : statistical properties, deviation from equilibrium, reversibility. On the other hand, we consider the properties of a granular gas maintained in a steady state, studying the fluctuations in the angular velocity of a blade immersed in the gas. We test some theoretical expectations for non dissipative systems and show that they are compatible with our measurements : fluctuation theorem, fluctuation-dissipation theorem. Using two coupled experimental devices, we discuss energy exchanges between systems maintained under different states, temperature or density, especially in the limit of very low density gases.Au cours des vingt dernières années, le formalisme en mécanique statistique permettant de décrire des états loin de l’équilibre s’est beaucoup développé. Cependant, les réalisations expérimentales permettant de tester les résultats, et leur robustesse lorsque le système s’éloigne des hypothèses dans le cadre desquelles ils sont établis, sont peu nombreuses et récentes. Partant de ce constat, nous proposons de considérer des systèmes macroscopiques qui permettent un bon contrôle des paramètres expérimentaux. Nous rapportons principalement l’étude de deux systèmes dissipatifs maintenus dans un état stationnaire.D’une part, nous étudions la dynamique d’une bille seule rebondissant à la verticale d’une surface vibrée. Nous considérons tout particulièrement les propriétés des échanges d’énergie entre la particule (la bille) et le thermostat (la surface vibrée) : propriétés statistiques, écart à la situation d’équilibre, réversibilité. D’autre part, nous considérons les propriétés d’un gaz granulaire maintenu dans un état stationnaire sondées au moyen des fluctuations de la position angulaire d’une pale plongée dans le système. Nous avons vérifions ainsi que certaines prédictions théoriques destinées à la description de systèmes non dissipatifs restent encore valables dans ce système dissipatif : théorème de fluctuations, théorème de fluctuation-dissipation, etc.L’utilisation de deux dispositifs expérimentaux couplés, nous permet, de plus, de discuter des échanges d’énergie entre des systèmes maintenus dans des conditions expérimentales différentes, température ou densité, en particulier dans la limite des gaz très raréfiés

La demande d’effacement de cicatrices cutanées

International audienceEn dermatologie, les progrès technologiques et leur médiatisation suscitent des demandes de plus en plus fréquentes d’effacement des cicatrices (cicatrices post–chirurgicales, cicatrices post-traumatiques, cicatrices d’acné, cicatrices auto-provoquées (excoriations, scarifications, automutilations) … Les attentes sont fortes et les demandes souvent pressantes chez ces patients qui ont une véritable souffrance avec sentiments de honte et culpabilité. Une réponse opératoire immédiate, sans entendre la demande latente derrière la demande d’effacement des cicatrices, risque d’aggraver la souffrance

Organic Matter in Space - an Overview

Organic compounds are ubiquitous in space: they are found in diffuse clouds, in the envelopes of evolved stars, in dense star-forming regions, in protoplanetary disks, in comets, on the surfaces of minor planets, and in meteorites and interplanetary dust particles. This brief overview summarizes the observational evidence for the types of organics found in these regions, with emphasis on recent developments. The Stardust sample-return mission provides the first opportunity to study primitive cometary material with sophisticated equipment on Earth. Similarities and differences between the types of compounds in different regions are discussed in the context of the processes that can modify them. The importance of laboratory astrophysics is emphasized.Comment: Introductory overview lecture presented at IAU Symposium 251, "Organic matter in space", held at Hong Kong, February 2008; to appear in IAU Symposium 251 proceedings, Cambridge University Press, ed. S. Kwok et a