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In toxicology, an Adverse Outcome Pathway (AOP) is a conceptual framework that qualitatively describes the existing knowledge on the links between the two anchor points: Mo- lecular Initiating Event (MIE) and Adverse Outcome (AO) at a level of biological organisation relevant for risk assessment. The transformation of an AOP to its quantitative version, qAOP allows to build a powerful risk assessment tool, thanks to its ability to quantitatively predict the AO. This paper presents a new method for modelling qAOP using Dynamic Bayesian Networks (DBN)., En toxicologie, un schéma de mode d’action (AOP : Adverse Outcome Pathway) est un cadre conceptuel qui décrit qualitativement les connaissances existantes concernant les liens entre deux points d’ancrage : un événement initiateur moléculaire (MIE : Molecular Initiating Event) et un résultat défavorable (AO : Adverse Outcome) à un niveau d’organisation biolo- gique pertinent pour l’évaluation du risque. La version quantitative d’un AOP, le qAOP, promet d’être un outil puissant pour l’évaluation des risques, grâce notamment à sa capacité de pré- diction. Cet article présente une méthode de modélisation originale de qAOPs par les réseaux bayésiens dynamiques.

We consider a spatio-temporal model to describe the spread of apple scab within an orchard composed of several plots. The model is defined on a regular lattice and evolves in continuous time. Based on ordinal categorical data observed only at some discrete instants, we adopt a continuous-time approach and apply a Bayesian framework for estimating unknown parameters.

International audience; An accurate weed management in a context of sustainable agriculture relies on the knowledge about spatial weed distribution within fields. To improve the representation of patchy spatial distributions of weeds, several sampling strategies are used and lead to various weed measurements (abundance, count, patch boundaries). Here, we propose a hierarchical Bayesian model which includes such multitype data and which allows the interpolation of weed spatial distributions (using a MCMC algorithm). The weed pattern is modeled with a log Gaussian Cox process and the various weed measurements are modeled with different observation processes. The application of the method to simulated data shows the advantage of combining several types of data (instead of using only one type of data). The method is also applied to infer the weed spatial distribution for real data.

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Hydrological calibration and prediction using conceptual models is affected by forcing/response data uncertainty and structural model error. The Bayesian Total Error Analysis methodology (BATEA) uses a hierarchical framework to represent individual sources of uncertainty. However, it is shown that standard multi-block Metropolis-within-Gibbs samplers commonly used in traditional Bayesian hierarchical Markov Chain Monte Carlo (MCMC) are exceedingly computationally expensive when applied to hydrologic models based on recursive numerical solution of coupled nonlinear differential equations describing the evolution of catchment states such as soil and groundwater storages. This note develops a limited-memory algorithm for accelerating multi-block MCMC sampling from the posterior distributions of such models using low-dimensional jump distributions. The new algorithm exploits the decaying memory of hydrological systems to provide accurate tolerance-based approximations of traditional fullmemory MCMC methods and is orders of magnitude more efficient than the latter.

Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution.

This thesis deals with maximum likelihood estimation in inverse problems. In the tree first chapters, we consider statistical models involving missing data in a parametric framework. Chapter 1 presents a version of the EM algorithm (Expectation Maximization), which combines a stochastic approximation with a Monte Carlo Markov Chain method: the missing data are drawn from a well-chosen transition probability. The almost sure convergence of the sequence generated by the algorithm to a local maximum of the likelihood of the observations is proved. Some applications to deconvolution and change-point detection are presented. Chapter 2 deals with the application of the algorithm to nonlinear mixed effects models. Besides the estimation of the parameters, we estimate the likelihood of the model and the Fisher information matrix. We assess the performance of the algorithm, comparing the results obtained with other methods, on examples coming from pharmacocinetics and pharmacodynamics. Chapter 3 presents an application to geophysics. We perform a joint inversion between teleseismic times and velocity and between gravimetric data and density. Our point of view is innovative because we estimate the parameters of the model which were generally fixed arbitrarily. Moreover we take into account a linear relation between slowness and density. Chapter 4 deals with non parametric density estimation in missing data problems. We propose a logspline estimator of the density of the non observed data, which maximizes the observed likelihood in a logspline model. We apply our algorithm in this parametric model. We study the convergence of this estimator to the density of the non observed data, when the size of the logpline model and the number of observations tend to infinity. Some applications illustrate this method., Cette thèse est consacrée à l'estimation par maximum de vraisemblance dans des problèmes inverses. Nous considérons des modèles statistiques à données manquantes, dans un cadre paramétrique au cours des trois premiers chapitres. Le Chapitre 1 présente une variante de l'algorithme EM (Expectation Maximization) qui combine une approximation stochastique à une méthode de Monte Carlo par chaînes de Markov : les données manquantes sont simulées selon une probabilité de transition bien choisie. Nous prouvons la convergence presque sûre de la suite générée par l'algorithme vers un maximum local de la vraisemblance des observations. Nous présentons des applications en déconvolution et en détection de ruptures. Dans le Chapitre 2, nous appliquons cet algorithme aux modèles non linéaires à effets mixtes et effectuons outre l'estimation des paramètres du modèle, des estimations de la vraisemblance du modèle et de l'information de Fisher. Les performances de l'algorithme sont illustrées via des comparaisons avec d'autres méthodes sur des exemples de pharmacocinétique et de pharmacodynamique. Le Chapitre 3 présente une application de l'algorithme en géophysique. Nous effectuons une inversion jointe, entre les temps de parcours des ondes sismiques et leurs vitesses et entre des mesures gravimétriques de surface et les densités du sous-sol, en estimant les paramètres du modèle, qui étaient en général fixés arbitrairement. De plus, nous prenons en compte une relation linéaire entre les densités et les vitesses des ondes. Le Chapitre 4 est consacré à l'estimation non paramétrique de la densité des données manquantes. Nous exhibons un estimateur logspline de cette densité qui maximise la vraisemblance des observations dans un modèle logspline et appliquons notre algorithme à ce modèle paramétrique. Nous étudions la convergence de cet estimateur vers la vraie densité lorsque la dimension du modèle logspline et le nombre d'observations tendent vers l'infini. Nous présentons quelques applications.