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Liste des exposés
I. Nouvelles tendances en mécanique des fluides
II. Problèmes à frontière libre
III. Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus
VI. Analyse et contrôle des EDP
VIII. Analyse non-lisse et optimisation
(cette liste est en processus d'actualisation)
List des exposés
1.
AZAïS Romain romain.azais@inria.fr
Inria Nancy, France
Titre: Statistical inference for conditioned critical Galton-Watson trees (details)
Inria Nancy, France
Titre: Statistical inference for conditioned critical Galton-Watson trees (details)
Résumé:
Many data are naturally described by an ordered tree structure: from blood vessels to XML files through the secondary structure of RNA. Conditioned Galton-Watson trees model a large variety of random hierarchical structures (Motzkin trees, Catalan trees, Cayley trees, etc). In this work, we introduce two strategies for estimating the variance parameter of a forest of critical conditioned Galton-Watson trees: least-square estimation and estimation by minimal Wasserstein distance. Both these procedures are based on the convergence of the contour process of a critical conditioned Galton-Watson tree towards the Brownian excursion. We investigate the asymptotic behavior of these estimates. The methodology is illustrated on both simulated and real datasets, with an application to determine the history of Wikipedia webpages.
Many data are naturally described by an ordered tree structure: from blood vessels to XML files through the secondary structure of RNA. Conditioned Galton-Watson trees model a large variety of random hierarchical structures (Motzkin trees, Catalan trees, Cayley trees, etc). In this work, we introduce two strategies for estimating the variance parameter of a forest of critical conditioned Galton-Watson trees: least-square estimation and estimation by minimal Wasserstein distance. Both these procedures are based on the convergence of the contour process of a critical conditioned Galton-Watson tree towards the Brownian excursion. We investigate the asymptotic behavior of these estimates. The methodology is illustrated on both simulated and real datasets, with an application to determine the history of Wikipedia webpages.
2.
CIUPERCA Gabriela Gabriela.Ciuperca@univ-lyon1.fr
Université Lyon 1, France
Titre: Détections de changements dans un modèle paramétrique (details)
Université Lyon 1, France
Titre: Détections de changements dans un modèle paramétrique (details)
Résumé:
On considère les deux types de modèles avec change-points: a posteriori et en temps réel. Les modèles avec change-points a posteriori sont analysés une fois que toutes les observations ont été réalisées. On se pose à ce moment-là la question si nous avons eu un seul modèle ou s'il y a eu plusieurs changements (phases), inconnus, dans le modèle. \\ Pour la détection en temps réel d'un changement, on étudie par des tests d'hypothèse si le modèle construit sur les données historiques change à chaque nouvelle observation mesurée.\\ Les fonctions de régression paramétriques de chaque phase du modèle peuvent être non linéaires ou linéaires. Dans le cas linéaire, le nombre de variables explicatives peut être très grand. Des résultats théoriques et des simulations seront présentés pour chaque type de modèle et chaque méthode d'inférence statistique. \\ Pour un modèle non linéaire a posteriori \[ Y_i= \sum^{K}_{r=0} g(X_i, \eb_{r+1}) \e1_{l_r \leq i < l_{r+1}}+ \varepsilon_i, \] les résultats obtenus par la technique du maximum de vraisemblance empirique (EMV) et la technique d'estimation quantile (on estime le nombre \(K\) de changements, leur location et le modèle de chaque phase) sont donnés. Toujours pour un modèle a posteriori, mais linéaire avec le nombre de variables explicatives \(X\) très grand, nous devons traiter en plus la question de sélection automatique des variables significatives. On étudie alors une méthode LASSO quantile adaptative. En plus, nous proposons un test non paramétrique basé sur le MVE, pour tester (a posteriori) si le modèle change.
On considère les deux types de modèles avec change-points: a posteriori et en temps réel. Les modèles avec change-points a posteriori sont analysés une fois que toutes les observations ont été réalisées. On se pose à ce moment-là la question si nous avons eu un seul modèle ou s'il y a eu plusieurs changements (phases), inconnus, dans le modèle. \\ Pour la détection en temps réel d'un changement, on étudie par des tests d'hypothèse si le modèle construit sur les données historiques change à chaque nouvelle observation mesurée.\\ Les fonctions de régression paramétriques de chaque phase du modèle peuvent être non linéaires ou linéaires. Dans le cas linéaire, le nombre de variables explicatives peut être très grand. Des résultats théoriques et des simulations seront présentés pour chaque type de modèle et chaque méthode d'inférence statistique. \\ Pour un modèle non linéaire a posteriori \[ Y_i= \sum^{K}_{r=0} g(X_i, \eb_{r+1}) \e1_{l_r \leq i < l_{r+1}}+ \varepsilon_i, \] les résultats obtenus par la technique du maximum de vraisemblance empirique (EMV) et la technique d'estimation quantile (on estime le nombre \(K\) de changements, leur location et le modèle de chaque phase) sont donnés. Toujours pour un modèle a posteriori, mais linéaire avec le nombre de variables explicatives \(X\) très grand, nous devons traiter en plus la question de sélection automatique des variables significatives. On étudie alors une méthode LASSO quantile adaptative. En plus, nous proposons un test non paramétrique basé sur le MVE, pour tester (a posteriori) si le modèle change.
3.
DEDU Silvia silvia.dedu@csie.ase.ro
Department of Applied Mathematics, Bucharest University of Economic Studies, Romania
Titre: Weighted power type probability distributions. Statistical properties and applications (details)
Department of Applied Mathematics, Bucharest University of Economic Studies, Romania
Titre: Weighted power type probability distributions. Statistical properties and applications (details)
Résumé:
In this paper a new class of weighted power type probability distributions is proposed. Its statistical properties are investigated, including moments, quantile and generating functions, order statistics and their moments and stochastic dominance. Maximum likelihood estimates are derived. The new distribution family is compared with other ones from the point of view of data modeling performances, by studying the inference with respect to other models. Some applications to modeling lifetime data are developed. The results obtained prove that the new class of distributions represents a more flexible family, with powerful statistical performances.
In this paper a new class of weighted power type probability distributions is proposed. Its statistical properties are investigated, including moments, quantile and generating functions, order statistics and their moments and stochastic dominance. Maximum likelihood estimates are derived. The new distribution family is compared with other ones from the point of view of data modeling performances, by studying the inference with respect to other models. Some applications to modeling lifetime data are developed. The results obtained prove that the new class of distributions represents a more flexible family, with powerful statistical performances.
4.
GAMBOA Fabrice fabrice.gamboa@math.univ-toulouse.fr
Institut de Mathématiques de Toulouse, France
Titre: Sensitivity analysis based on Cramér von Mises distance (details)
Institut de Mathématiques de Toulouse, France
Titre: Sensitivity analysis based on Cramér von Mises distance (details)
Résumé:
We first study a new sensitivity index based on higher moments generalising the so-called Sobol one. Further, we define and study a new sensitivity index based on the Cramér von Mises distance. This new index appears to be more general than the Sobol one as it takes into account, not only the variance, but the whole distribution of the random variable. Furthermore, we study the statistical properties of a Monte Carlo estimate of this new index.
We first study a new sensitivity index based on higher moments generalising the so-called Sobol one. Further, we define and study a new sensitivity index based on the Cramér von Mises distance. This new index appears to be more general than the Sobol one as it takes into account, not only the variance, but the whole distribution of the random variable. Furthermore, we study the statistical properties of a Monte Carlo estimate of this new index.
5.
MONTUELLE Lucie montuelle@math.univ-paris-diderot.fr
Université Paris Diderot, France
Titre: Short-term wind power forecasting (details)
Université Paris Diderot, France
Titre: Short-term wind power forecasting (details)
Résumé:
Wind power forecasting is a problem in touch with economic, industrial and environmental challenges. In the framework of the ANR project Forewer, real-time wind power forecast on a wind farm has been considered, based on meteorological data. Machine learning technics have been tested and compared to parametric models, close to the physical model. On the studied data set, learning methods, especially well-calibrated Random Forests, have shown the best performances. Moreover, our procedure seems robust to the error on the wind speed measure. This work has been conducted with A. Fischer, M. Mougeot et D. Picard. Aurélie Fischer, Lucie Montuelle, Mathilde Mougeot, Dominique Picard, \emph{Real-time wind power forecast},Preprint, 2016
Wind power forecasting is a problem in touch with economic, industrial and environmental challenges. In the framework of the ANR project Forewer, real-time wind power forecast on a wind farm has been considered, based on meteorological data. Machine learning technics have been tested and compared to parametric models, close to the physical model. On the studied data set, learning methods, especially well-calibrated Random Forests, have shown the best performances. Moreover, our procedure seems robust to the error on the wind speed measure. This work has been conducted with A. Fischer, M. Mougeot et D. Picard. Aurélie Fischer, Lucie Montuelle, Mathilde Mougeot, Dominique Picard, \emph{Real-time wind power forecast},Preprint, 2016
6.
ROBE-VOINEA Elena-gratiela elena_robe@yahoo.com
University of Bucharest, Romania
Titre: Multivariate aggregate claims evaluation using the Fast Fourier Transform (details)
University of Bucharest, Romania
Titre: Multivariate aggregate claims evaluation using the Fast Fourier Transform (details)
Résumé:
The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this talk, we extend it to a multivariate model that includes losses of different types and some dependency between them. Since the Fourier transform method works with truncated distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To avoid such problems, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.
The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this talk, we extend it to a multivariate model that includes losses of different types and some dependency between them. Since the Fourier transform method works with truncated distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To avoid such problems, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.
7.
ROCHE Angelina roche@ceremade.dauphine.fr
Université Paris Dauphine, France
Titre: Kernel adaptive estimation for functional data (details)
Université Paris Dauphine, France
Titre: Kernel adaptive estimation for functional data (details)
Résumé:
The aim is to study the relationship between a real variable of interest \(Y\) and a functional variable \(X\) (that is to say a random variable taking values in a function space). This type of problem appears, for example, in spectroscopy, when trying to infer the chemical composition of a product from its spectrometric curve. We consider Nadaraya-Watson type kernel estimators of the conditional distribution function and of the regression function. The quality of estimators heavily depends on the choice of a parameter: the bandwidth. We propose a method for selecting this parameter, inspired by the work of Goldenshluger and Lepski (2011). The resulting estimator is optimal in the sense of the oracle and in the minimax sense, up to a log loss.
The aim is to study the relationship between a real variable of interest \(Y\) and a functional variable \(X\) (that is to say a random variable taking values in a function space). This type of problem appears, for example, in spectroscopy, when trying to infer the chemical composition of a product from its spectrometric curve. We consider Nadaraya-Watson type kernel estimators of the conditional distribution function and of the regression function. The quality of estimators heavily depends on the choice of a parameter: the bandwidth. We propose a method for selecting this parameter, inspired by the work of Goldenshluger and Lepski (2011). The resulting estimator is optimal in the sense of the oracle and in the minimax sense, up to a log loss.
8.
STOICA Radu radu.stoica@univ-lille1.fr
Universite de Lille, France
Titre: Spatial data analysis through probabilistic modelling and statistical inference (details)
Universite de Lille, France
Titre: Spatial data analysis through probabilistic modelling and statistical inference (details)
Résumé:
\documentclass[11pt,twoside]{article} \usepackage[utf8]{inputenc} \usepackage{amsthm,amsmath,amssymb,epsf} %%% FOR THE GRAPHICS %% \usepackage{graphicx,color} %\usepackage[normal]{subfig} \usepackage{subfig} %\usepackage{array,multirow} \usepackage{array} \begin{document} \thispagestyle{empty} \begin{center} {\LARGE Spatial data analysis through probabilistic modelling and statistical inference}\\[.5in] {\large R. S. Stoica \footnote{radu.stoica@univ-lille1.fr}}\\[.2in] {\em Université de Lille, Laboratoire Paul Painlevé\\ 59655 Villeneuve d'Ascq Cedex, France}\\[.1in] {\em Institut de Mécanique Céleste et Calcul des Ephémérides\\ Observatoire de Paris, 75014 Paris, France} \end{center} \noindent Spatial data is made of elements having two components: position in an observation domain and characteristic measured or associated with the given position. In this presentation several examples of such data sets are showed: road networks evolution in forest exploitations, the gravity centre positions of a binary asteroid system, the coordinates of the artificial spatial debris around the Earth, the map of the planetary perturbations affecting the comets dynamics, the galaxy centres observed in a region of our Universe. The particulaor structure of the data, {\it i.e.} spatial coordinate and associate mark, induces that the question almost always arising in such a data analysis is what is the pattern hidden in the data? The answers to this type of questions may be given using methodology based on probabilistic and statistical theory: summary statistics, modelling, MCMC simulation, statistical inference and results evaluation. A brief presentation of some of these tools, especially adapted for the application on the previously cited examples, it will be given.\\ ~\\ \end{document}
\documentclass[11pt,twoside]{article} \usepackage[utf8]{inputenc} \usepackage{amsthm,amsmath,amssymb,epsf} %%% FOR THE GRAPHICS %% \usepackage{graphicx,color} %\usepackage[normal]{subfig} \usepackage{subfig} %\usepackage{array,multirow} \usepackage{array} \begin{document} \thispagestyle{empty} \begin{center} {\LARGE Spatial data analysis through probabilistic modelling and statistical inference}\\[.5in] {\large R. S. Stoica \footnote{radu.stoica@univ-lille1.fr}}\\[.2in] {\em Université de Lille, Laboratoire Paul Painlevé\\ 59655 Villeneuve d'Ascq Cedex, France}\\[.1in] {\em Institut de Mécanique Céleste et Calcul des Ephémérides\\ Observatoire de Paris, 75014 Paris, France} \end{center} \noindent Spatial data is made of elements having two components: position in an observation domain and characteristic measured or associated with the given position. In this presentation several examples of such data sets are showed: road networks evolution in forest exploitations, the gravity centre positions of a binary asteroid system, the coordinates of the artificial spatial debris around the Earth, the map of the planetary perturbations affecting the comets dynamics, the galaxy centres observed in a region of our Universe. The particulaor structure of the data, {\it i.e.} spatial coordinate and associate mark, induces that the question almost always arising in such a data analysis is what is the pattern hidden in the data? The answers to this type of questions may be given using methodology based on probabilistic and statistical theory: summary statistics, modelling, MCMC simulation, statistical inference and results evaluation. A brief presentation of some of these tools, especially adapted for the application on the previously cited examples, it will be given.\\ ~\\ \end{document}
9.
TOMA Aida aida_toma@yahoo.com
Bucharest Academy of Economic Studies, Romania
Titre: Minimum dual divergence estimators for moment condition models (details)
Bucharest Academy of Economic Studies, Romania
Titre: Minimum dual divergence estimators for moment condition models (details)
Résumé:
The minimum dual divergence estimators and tests for moment condition models have been proposed recently in literature. The main advantage, of using a divergence based approach and duality, lays in the fact that it leads to asymptotic properties of the estimators and test statistics under the model, as well as under the alternative including misspecification, which cannot be achieved through the classical empirical likelihood context. Also, the estimators are asymptotically the best in the sense on Hansen yielding a “smallest” asymptotic covariance matrix. On the other hand, the estimators of the unknown parameter corresponding to the model have bounded influence functions if and only if the function inducing the orthogonality conditions of the model is bounded. Since in many applications this function is not bounded, it is useful to have procedures that modify the orthogonality conditions in order to obtain robust versions of the estimators. In this paper we propose robust versions of the minimum dual divergence estimators using truncated orthogonality functions. We prove robustness properties and asymptotic properties of the new estimation method, underlying some advantages of using it with respect to other known methods. The performance of the new method is illustrated through Monte Carlo simulations for some moment condition model.
The minimum dual divergence estimators and tests for moment condition models have been proposed recently in literature. The main advantage, of using a divergence based approach and duality, lays in the fact that it leads to asymptotic properties of the estimators and test statistics under the model, as well as under the alternative including misspecification, which cannot be achieved through the classical empirical likelihood context. Also, the estimators are asymptotically the best in the sense on Hansen yielding a “smallest” asymptotic covariance matrix. On the other hand, the estimators of the unknown parameter corresponding to the model have bounded influence functions if and only if the function inducing the orthogonality conditions of the model is bounded. Since in many applications this function is not bounded, it is useful to have procedures that modify the orthogonality conditions in order to obtain robust versions of the estimators. In this paper we propose robust versions of the minimum dual divergence estimators using truncated orthogonality functions. We prove robustness properties and asymptotic properties of the new estimation method, underlying some advantages of using it with respect to other known methods. The performance of the new method is illustrated through Monte Carlo simulations for some moment condition model.
Participants
1.
LACAUX Céline Celine.Lacaux@univ-avignon.fr
Avignon Université, France
Avignon Université, France