Le travail est consacré aux questions de la statistique des processus stochastiques. Particulièrement, on considère deux problèmes d'estimation. Le premier chapitre se concentre sur le problème d'estimation non-paramétrique pour le processus de Poisson non-homogène. On estime la fonction moyenne de ce processus, donc le problème est dans le domaine d'estimation non-paramétrique. On commence par la définition de l'efficacité asymptotique dans les problèmes non-paramétriques et on procède à exploration de l'existence des estimateurs asymptotiquement efficaces. On prend en considération la classe des estimateurs à noyau. Dans la thèse il est démontré que sous les conditions sur les coefficients du noyau par rapport à une base trigonométrique, on a l'efficacité asymptotique dans le sens minimax sur les ensembles divers. Les résultats obtenus soulignent le phénomène qu'en imposant des conditions de régularité sur la fonction inconnue, on peut élargir la classe des estimateurs asymptotiquement efficaces. Pour comparer les estimateurs asymptotiquement efficaces (du premier ordre), on démontre une inégalité qui nous permet de trouver un estimateur qui est asymptotiquement efficace du second ordre. On calcule aussi la vitesse de convergence pour cet estimateur, qui dépend de la régularité de la fonction inconnue et finalement on calcule la valeur minimale de la variance asymptotique pour cet estimateur. Cette valeur joue le même rôle dans l'estimation du second ordre que la constantede Pinsker dans le problème d'estimation de la densité ou encore l'information de Fisher dans les problèmes d'estimation paramétrique.Le deuxième chapitre est dédié au problème de l’estimation de la solution d’une équation différentielle stochastique rétrograde (EDSR). On observe un processus de diffusion qui est donnée par son équation différentielle stochastique dont le coefficient de la diffusion dépend d’un paramètre inconnu. Les observations sont discrètes. Pour estimer la solution de l’EDSR on a besoin d’un estimateur-processus pour leparamètre, qui, chaque instant n’utilise que la partie des observations disponible. Dans la littérature il existe une méthode de construction, qui minimise une fonctionnelle. On ne pouvait pas utiliser cet estimateur, car le calcul serait irréalisable. Dans le travail nous avons proposé un estimateur-processus qui a la forme simple et peut être facilement calculé. Cet estimateur-processus est un estimateur asymptotiquementefficace et en utilisant cet estimateur on estime la solution de l’EDSR de manière efficace aussi. / This work is devoted to the questions of the statistics of stochastic processes. Particularly, the first chapter is devoted to a non-parametric estimation problem for an inhomogeneous Poisson process. The estimation problem is non-parametric due to the fact that we estimate the mean function. We start with the definition of the asymptotic efficiency in non-parametric estimation problems and continue with examination of the existence of asymptotically efficient estimators. We consider a class of kernel-type estimators. In the thesis we prove that under some conditions on the coefficients of the kernel with respect to a trigonometric basis we have asymptotic efficiency in minimax sense over various sets. The obtained results highlight the phenomenon that imposing regularity conditions on the unknown function, we can widen the class ofasymptotically efficient estimators. To compare these (first order) efficient estimators, we prove an inequality which allows us to find an estimator which is asymptotically efficient of second order. We calculate also the rate of convergence of this estimator, which depends on the regularity of the unknown function, and finally the minimal value of the asymptotic variance for this estimator is calculated. This value plays the same role in the second order estimation as the Pinsker constant in the density estimation problem or the Fisher information in parametric estimation problems. The second chapter is dedicated to a problem of estimation of the solution of a Backward Stochastic Differential Equation (BSDE). We observe a diffusion process which is given by its stochastic differential equation with the diffusion coefficientdepending on an unknown parameter. The observations are discrete. To estimate the solution of a BSDE, we need an estimator-process for a parameter, which, for each given time, uses only the available part of observations. In the literature there exists a method of construction, which minimizes a functional. We could not use this estimator, because the calculations would not be feasible. We propose an estimator-process which has a simple form and can be easily computed. Using this estimator we estimate the solution of a BSDE in an asymptotically efficient way.

Radio astronomy is the science of observing the universe at radio frequencies. In recent years, radio astronomy has faced a growing interference problem as radio frequency (RF) bandwidth has become an increasingly scarce commodity. Communication systems such as Earth orbiting communication satellites creates severe interference to the radio telescopes. This thesis proposes an algorithm to mitigate the radio frequency interference (RFI) from the Iridium satellite system. A technique is presented here to detect the downlink signal of Iridium, estimate the parameters of the signal, synthesize the noise-free version of the signal and finally subtract the recreated signal from the radio telescope output. Using both simulated and real data captured by a radio telescope testbed, we demonstrate that for Iridium bursts with 20 dB signal to noise power ratio (SNR), the proposed algorithm achieves more than 15 dB cancellation. The method proposed here can be implemented using present-day digital signal processing hardware and software. A performance analysis of this proposed cancellation scheme in the radio astronomy RFI mitigation regime is presented. / Master of Science

Dans cette thèse, on considère une équation différentielle stochastique gouvernée par un processus de Lévy de saut pur dont l’indice d’activité des sauts α ∈ (0, 2) et on observe des données haute fréquence de ce processus sur un intervalle de temps fixé. Cette thèse est consacrée tout d’abord à l’étude du comportement de la densité du processus en temps petit. Ces résultats permettent ensuite de montrer la propriété LAMN (Local Asymptotic Mixed Normality) pour les paramètres de dérive et d’échelle. Enfin, on étudie des estimateurs de l’indice α du processus.La première partie traite du comportement asymptotique de la densité en temps petit du processus. Le processus est supposé dépendre d’un paramètre β = (θ,σ) et on étudie, dans cette partie, la sensibilité de la densité par rapport à ce paramètre. Cela étend les résultats de [17] qui étaient restreints à l’indice α ∈ (1,2) et ne considéraient que la sensibilité par rapport au paramètre de dérive. En utilisant le calcul de Malliavin, on obtient la représentation de la densité, de sa dérivée et de sa dérivée logarithmique comme une espérance et une espérance conditionnelle. Ces formules de représentation font apparaître des poids de Malliavin dont les expressions sont données explicitement, ce qui permet d’analyser le comportement asymptotique de la densité en temps petit, en utilisant la propriété d’autosimilarité du processus stable.La deuxième partie de cette thèse concerne la propriété LAMN (Local Asymptotic Mixed Normality) pour les paramètres. Le coefficient de dérive et le coefficient d’échelle dépendent tous les deux de paramètres inconnus et on étend les résultats de [17]. On identifie l’information de Fisher asymptotique ainsi que les vitesses optimales de convergence. Ces quantités dépendent de l’indice αLa troisième partie propose des estimateurs pour l’indice d’activité des sauts α ∈ (0,2) basés sur des méthodes de moments qui généralisent les résultats de Masuda [53]. On montre la consistence et la normalité asymptotique des estimateurs et on illustre les résultats par des simulations numériques / In this thesis, we consider a stochastic differential equation driven by a truncated pure jump Lévy process with index α ∈(0,2) and observe high frequency data of the process on a fixed observation time. We first study the behavior of the density of the process in small time. Next, we prove the Local Asymptotic Mixed Normality (LAMN) property for the drift and scaling parameters from high frequency observations. Finally, we propose some estimators of the index parameter of the process.The first part deals with the asymptotic behavior of the density in small time of the process. The process is assumed to depend on a parameter β = (θ,σ) and we study, in this part, the sensitivity of the density with respect to this parameter. This extends the results of [17] which were restricted to the index α ∈ (1,2) and considered only the sensitivity with respect to the drift coefficient. By using Malliavin calculus, we obtain the representation of the density, its derivative and its logarithm derivative as an expectation and a conditional expectation. These representation formulas involve some Malliavin weights whose expressions are given explicitly and this permits to analyze the asymptotic behavior in small time of the density, using the self-similarity property of the stable process.The second part of this thesis concerns the Local Asymptotic Mixed Normality property for the parameters. Both the drift coefficient and scale coefficient depend on the unknown parameters. Extending the results of [17], we compute the asymptotic Fisher information and find that the rate in the Local Asymptotic Mixed Normality property depends on the index α.The third part proposes some estimators of the jump activity index α ∈ (0,2) based on the method of moments as in Masuda [53]. We prove the consistency and asymptotic normality of the estimators and give some simulations to illustrate the finite-sample behaviors of the estimators

Un système est souvent caractérisé par plusieurs modes de fonctionnement, chacun pouvant alors être décrit par un modèle qui lui est propre. Dans le cas où la commutation entre les modes de fonctionnement résulte d'un processus inconnu (un défaut, un changement de condition,...), il est difficile de manipuler ces systèmes et d'appliquer les commandes appropriées. Cette thèse traite du problème de la détection du changement de mode d'un système. A partir d'un système partiellement supervisé (connaissance du nombre de mode de fonctionnement du système ainsi que de la structure du modèle représentant chaque mode), une méthode est développée pour détecter le mode de fonctionnement actif du système à chaque instant. Pour cela, l'analyse du gradient des résidus obtenu par la multiplication des modèles locaux entre-eux, permet de caractériser le mode de fonctionnement. Une application de cette méthode est réalisée sur des données simulées et réelles de coulée continue de l'acier, afin de détecter un phénomène particulier : le collage. Finalement, une méthode par rejet de mode est mise en place sur des données réelles thermiques dans le même but (la détection des collages en lingotière de coulée continue) / Most of time a system is characterized by few operating modes, each of them could be describe by a model. In the case of the commutation between each operating mode is due to unknown process (fault, changing in condition,) it could be difficult to operate with this system and used the appropriate commands. With a partially supervised system (knowing of number of operating mode and model structure that represent each mode), a method is developed to detect the active operating mode at each time. Indeed, the analyses of the residual gradient, that obtain by product each local model together, permit to characterize the operating mode. Application of this method is presented with simulated data and industrial data of continuous casting to detect a particular phenomenon: the sticker. Finally, a rejection mode method is used on industrial thermal data in the same aim (detection of stickers in continuous casting)

O projeto de engenharia é desenvolvido baseado em um modelo de comportamento da estrutura a ser construída. Por sua vez, este modelo incorpora uma série de hipóteses de trabalho que, durante a fase de construção ou de utilização da obra, podem não ser observadas na sua totalidade. Dentro deste cenário, a retroanálise probabilista mostra-se uma ferramenta poderosa para avaliação contínua das hipóteses de trabalho durante a construção e toda a vida útil da estrutura, uma vez que permite incorporar novas informações ao modelo inicial através de métodos formalizados. Este trabalho apresenta uma revisão da retroanálise probabilista e sua aplicação prática na atualização do campo de permeabilidades de uma barragem de terra existente, com base em leituras piezométricas. Os resultados do estudo permitiram rever os valores dos parâmetros do modelo adotado, isto é, as permeabilidades dos diversos materiais, sugerindo ao mesmo tempo a aceitação do próprio modelo. Um estudo paramétrico destaca a importância relativa, para a retroanálise probabilista, das diversas variáveis envolvidas, indicando assim áreas em que a investigação complementar é mais necessária. / The engineering project is based upon a model that can predict the behavior of the facility to be constructed. Such model incorporates a series of working hypotheses which may or may not be fully realized during construction or operation. Under such circumstances, probabilistic back-analysis is a powerful tool for continuous evaluation of the working hypotheses, during construction and throughout the lifespan of the structure, given that it provides for the formal updating of the initial model and its parameters on the basis of incoming information. This study presents a review of probabilistic back-analysis and a practical application to the updating of the permeability field of an earth embankment, on the basis of piezometer readings. Results of the study led to updating of the parameters of the adopted model, that is, permeabilities of the several materials, while suggesting acceptance of the model itself. A parametric study reveals the relative importance of the several variables involved in the probabilistic back-analysis, thus indicating areas in which complementary research is mostly needed.

A utilização de modelos de teletrafego que contemplem caractersticas tais como autossimilaridade e dependencia de longa duraçao tem se mostrado cada vez mais como sendo ponto-chave na correta caracterizaçao do teletrafego Local Area Network (LAN) e Wide Area Network (WAN) [1, 2]. Tal caracterizaçao e necessaria para o monitoramento e controle de teletrafego em redes convergentes [3]. Nesse contexto, a questão da estimaçao precisa do parâmetro de autossimilaridade, denominado de parâmetro de Hurst, torna-se essencial. Entretanto, estudos comprovam que, alem da dependência de longa duraçao, redes WAN podem, não raramente, apresentar caractersticas mistas de dependência de longa e de curta duraçao [4, 5]. Enquanto vasta literatura cientca, tanto teorica como pratica, tem abordado com anco a questão da acuracia de diversos estimadores para o parâmetro de Hurst [6, 7, 8, 9], pouca atenção tem sido dada a questão da estimação deste parâmetro na presenca de dependência de curta duração. O presente trabalho de pesquisa concentrou-se no estudo dos metodos de estimaçao do parametro de Hurst baseados no espectro wavelet, em particular atraves do metodo de Abry-Veitch [10] { baseado na transformada Discrete Wavelet Transform (DWT) { e atraves do espectro obtido atraves da transformada Discrete Wavelet Packet Transform (DWPT). Os resultados baseados no metodo de Abry-Veitch demonstram que, atraves de um ajuste apropriado dos par^ametros de estimaçao, tal metodo permite uma estimaçao robusta na presenca de componentes com dependencia de curta duraçao, mesmo em situaçoes de mudanca de regime de tal componente, caracterstica desejavel para a estimaçao em tempo real do parametro de Hurst. Entretanto, a dispersao consideravel apresentada, em alguns casos, pelas estimativas do metodo de Abry-Veitch, motivou o estudo da utilizaçao do espectro wavelet obtido via transformada DWPT para realizaçao da estimaçao do parametro de Hurst. Os resultados indicam que a utilizaçao de tal transformada gera um espectro wavelet tal que e possvel detectar a presenca ou não de componentes com dependencia de curta duraçao. Ao final, os resultados da pesquisa realizada são sumarizados e utilizados em uma proposta de mecanismo de estimaçao do parametro de Hurst em tempo real, na presenca simultanea de componentes de dependencia de longa e curta duracão. / The use of network trac models that hold self-similar and long-range dependence characteristics have shown to be a key element on the correct characterization of Local Area Network (LAN) and Wide Area Network (WAN) network trac [1, 2]. Such characterization is necessary to monitor and control the network trac in converged networks [3]. In this context, the accurate estimation of the selfsimilarity parameter, named Hurst parameter, is a major issue. However, studies show that, besides the long-range dependence, WAN network trac may, not uncommonly, present mixed long and short-range dependence characteristics [4, 5]. While great part of either theoretical or practical scientic literature has been focused on the issue of Hurst parameter estimator accuracy [6, 7, 8, 9], little attention has been given to the estimation of such parameter in the presence of short-range dependence. This research work has focused on the study of the Hurst parameter estimation methods based on the wavelet spectrum, specially through the Abry-Veitch method [10] { which is based on the Discrete Wavelet Transform (DWT) transform { and through the wavelet spectrum based on the Discrete Wavelet Packet Transform (DWPT) transform. The results based on the Abry-Veitch method show that, through a suitable adjustment of the estimation parameters, such method yields a robust estimation in the presence of short-range dependence components, even in changing conditions of such component, a desirable characteristic for the real-time estimation of the Hurst parameter. However, the signi cant dispersion presented, occasionally, by the Abry-Veitch method estimates motivated the research of the usage of the wavelet spectrum obtained via DWPT transform to estimate the Hurst parameter. The results show that the usage of such transform generates such a wavelet spectrum that it is possible to detect whether short-range dependence components are present, or not, in the analyzed series. At the end, the research results are summarized and used to propose a realtime Hurst parameter estimation mechanism, in the presence of simultaneous long- and short-range dependence components.

A utilização de modelos de teletrafego que contemplem caractersticas tais como autossimilaridade e dependencia de longa duraçao tem se mostrado cada vez mais como sendo ponto-chave na correta caracterizaçao do teletrafego Local Area Network (LAN) e Wide Area Network (WAN) [1, 2]. Tal caracterizaçao e necessaria para o monitoramento e controle de teletrafego em redes convergentes [3]. Nesse contexto, a questão da estimaçao precisa do parâmetro de autossimilaridade, denominado de parâmetro de Hurst, torna-se essencial. Entretanto, estudos comprovam que, alem da dependência de longa duraçao, redes WAN podem, não raramente, apresentar caractersticas mistas de dependência de longa e de curta duraçao [4, 5]. Enquanto vasta literatura cientca, tanto teorica como pratica, tem abordado com anco a questão da acuracia de diversos estimadores para o parâmetro de Hurst [6, 7, 8, 9], pouca atenção tem sido dada a questão da estimação deste parâmetro na presenca de dependência de curta duração. O presente trabalho de pesquisa concentrou-se no estudo dos metodos de estimaçao do parametro de Hurst baseados no espectro wavelet, em particular atraves do metodo de Abry-Veitch [10] { baseado na transformada Discrete Wavelet Transform (DWT) { e atraves do espectro obtido atraves da transformada Discrete Wavelet Packet Transform (DWPT). Os resultados baseados no metodo de Abry-Veitch demonstram que, atraves de um ajuste apropriado dos par^ametros de estimaçao, tal metodo permite uma estimaçao robusta na presenca de componentes com dependencia de curta duraçao, mesmo em situaçoes de mudanca de regime de tal componente, caracterstica desejavel para a estimaçao em tempo real do parametro de Hurst. Entretanto, a dispersao consideravel apresentada, em alguns casos, pelas estimativas do metodo de Abry-Veitch, motivou o estudo da utilizaçao do espectro wavelet obtido via transformada DWPT para realizaçao da estimaçao do parametro de Hurst. Os resultados indicam que a utilizaçao de tal transformada gera um espectro wavelet tal que e possvel detectar a presenca ou não de componentes com dependencia de curta duraçao. Ao final, os resultados da pesquisa realizada são sumarizados e utilizados em uma proposta de mecanismo de estimaçao do parametro de Hurst em tempo real, na presenca simultanea de componentes de dependencia de longa e curta duracão. / The use of network trac models that hold self-similar and long-range dependence characteristics have shown to be a key element on the correct characterization of Local Area Network (LAN) and Wide Area Network (WAN) network trac [1, 2]. Such characterization is necessary to monitor and control the network trac in converged networks [3]. In this context, the accurate estimation of the selfsimilarity parameter, named Hurst parameter, is a major issue. However, studies show that, besides the long-range dependence, WAN network trac may, not uncommonly, present mixed long and short-range dependence characteristics [4, 5]. While great part of either theoretical or practical scientic literature has been focused on the issue of Hurst parameter estimator accuracy [6, 7, 8, 9], little attention has been given to the estimation of such parameter in the presence of short-range dependence. This research work has focused on the study of the Hurst parameter estimation methods based on the wavelet spectrum, specially through the Abry-Veitch method [10] { which is based on the Discrete Wavelet Transform (DWT) transform { and through the wavelet spectrum based on the Discrete Wavelet Packet Transform (DWPT) transform. The results based on the Abry-Veitch method show that, through a suitable adjustment of the estimation parameters, such method yields a robust estimation in the presence of short-range dependence components, even in changing conditions of such component, a desirable characteristic for the real-time estimation of the Hurst parameter. However, the signi cant dispersion presented, occasionally, by the Abry-Veitch method estimates motivated the research of the usage of the wavelet spectrum obtained via DWPT transform to estimate the Hurst parameter. The results show that the usage of such transform generates such a wavelet spectrum that it is possible to detect whether short-range dependence components are present, or not, in the analyzed series. At the end, the research results are summarized and used to propose a realtime Hurst parameter estimation mechanism, in the presence of simultaneous long- and short-range dependence components.

We consider the problem of estimating the failure stresses of bundles (i.e. the tensile forces that destroy the bundles), constructed of several statisti-cally similar fibres, given a particular kind of censored data. Each bundle consists of several fibres which have their own independent identically dis-tributed failure stresses, and where the force applied on a bundle at any moment is distributed equally between the unbroken fibres in the bundle. A bundle with these properties is an example of an equal load-sharing sys-tem, often referred to as the Daniels failure model. The testing of several bundles generates a special kind of censored data, which is complexly struc-tured. Strongly consistent non-parametric estimators of the distribution laws of bundles are obtained by applying the theory of martingales, and by using the observed data. It is proved that random sampling, with replace-ment from the statistical data related to each tested bundle, can be used to obtain asymptotically correct estimators for the distribution functions of deviations of non-parametric estimators from true values. In the case when the failure stresses of the fibres are described by a Weibull distribution, we obtain strongly consistent parametric maximum likelihood estimators of the distribution functions of failure stresses of bundles, by using the complexly structured data. Numerical examples illustrate the behavior of the obtained estimators.

Face aux enjeux climatiques actuels, le secteur bâtiment est encouragé à réduire sa consommation énergétique tout en préservant le confort des occupants. C’est dans ce contexte que s’inscrit le projet ANR PRECCISION qui vise au développement d’outils et de méthodes pour la gestion énergétique optimisée des bâtiments qui nécessitent l’utilisation de modèles thermiques dynamiques. Les travaux de thèse, effectués entre le G2Elab et le G-SCOP, se sont focalisés sur les problématiques liées à l’estimation paramétrique de ces modèles. En effet, les incertitudes liées aux phénomènes mal maîtrisés et la nature des modèles rendent le calibrage des paramètres des modèles délicat. Cette procédure complexe n’est à ce jour pas systématisable : les modèles auto-regressifs ont une faible capacité d'extrapolation car leur structure est inadaptée, tandis que les modèles physiques sont non-linéaires par rapport à de nombreux paramètres : les estimations conduisent à des optimums locaux fortement dépendant de l'initialisation. Pour lever ce verrou, plusieurs approches ont été explorées à partir de modèles physiques adaptés pour lesquels des études sur l’identifiabilité ont été menées sur une plateforme expérimentale : PREDIS MHI. Différentes stratégies d'optimisation sont alors proposées visant à déterminer les paramètres qui peuvent être recalés. La première approche repose sur une analyse a priori de la dispersion paramétrique, la seconde repose sur une procédure de méta-optimisation qui détermine dynamiquement, au fur et à mesure d'une séquence d'optimisations, les paramètres à recaler. Les résultats sont analysés et comparés à diverses approches (modèles universels, identification « naïve » de tous les paramètres d’un modèle physique, algorithme génétique, …) à travers différents cas d'application. / In order to tackle the actual climate issues, the building field is encouraged to reduce his energetic consumption without changing the occupant’s comfort. In this context, the aim of the ANR PRECCISION project is to develop tools and methods for energetic management of the buildings which needs the use of dynamical thermal models. The PHD works, realise between the G2Elab and the G-SCOP, was focused on models parametric estimation issues. Indeed, uncertainties due to unknown phenomena and the nature of models lead to difficulties for the calibration of the models. Nowadays, this complex procedure is still not automatable: auto-regressive models have a low capacity to extrapolate because of their inadequate structure, whereas the physical models are non-linear regarding many parameters: estimations lead towards local optimums which highly depend on the initial point. In order to eliminate these constraints, several approaches have been explored with physical models adapted for which identifiability studies have been reached on an experimental platform: PREDIS MHI. Different optimisation strategies will be proposed in order to determine the parameters which can be estimated. The first approach uses an analyse a priori of the parametric dispersion, the second one use a meta optimisation which dynamicaly determined as the optimisation sequence, the parameters which can be readjusted. The results are analysed and compared to several approaches (universal models, “simple” identification of all the parameters of a physical model, genetic algorithm …) in different application cases.

O projeto de engenharia é desenvolvido baseado em um modelo de comportamento da estrutura a ser construída. Por sua vez, este modelo incorpora uma série de hipóteses de trabalho que, durante a fase de construção ou de utilização da obra, podem não ser observadas na sua totalidade. Dentro deste cenário, a retroanálise probabilista mostra-se uma ferramenta poderosa para avaliação contínua das hipóteses de trabalho durante a construção e toda a vida útil da estrutura, uma vez que permite incorporar novas informações ao modelo inicial através de métodos formalizados. Este trabalho apresenta uma revisão da retroanálise probabilista e sua aplicação prática na atualização do campo de permeabilidades de uma barragem de terra existente, com base em leituras piezométricas. Os resultados do estudo permitiram rever os valores dos parâmetros do modelo adotado, isto é, as permeabilidades dos diversos materiais, sugerindo ao mesmo tempo a aceitação do próprio modelo. Um estudo paramétrico destaca a importância relativa, para a retroanálise probabilista, das diversas variáveis envolvidas, indicando assim áreas em que a investigação complementar é mais necessária. / The engineering project is based upon a model that can predict the behavior of the facility to be constructed. Such model incorporates a series of working hypotheses which may or may not be fully realized during construction or operation. Under such circumstances, probabilistic back-analysis is a powerful tool for continuous evaluation of the working hypotheses, during construction and throughout the lifespan of the structure, given that it provides for the formal updating of the initial model and its parameters on the basis of incoming information. This study presents a review of probabilistic back-analysis and a practical application to the updating of the permeability field of an earth embankment, on the basis of piezometer readings. Results of the study led to updating of the parameters of the adopted model, that is, permeabilities of the several materials, while suggesting acceptance of the model itself. A parametric study reveals the relative importance of the several variables involved in the probabilistic back-analysis, thus indicating areas in which complementary research is mostly needed.