Search

National audience; Jacques Bernier was an engineer at the French Electricity Company (EDF). He pioneered a course on statistical decision at ISUP. I can witness the qualities of his course which I enjoyed when following as a former student of his. Since he retired in 1991, Jacques Bernier kept his scientific activities. He continues publishing articles in applied Bayesian statistics. He counts among the statisticians who contributed the most to the diffusion and the demonstration of the potential of a Bayesian approach in hydrology.His disciple Éric Parent belongs to the French civil corps of Bridge, Road, Water and Forest Engineers. He presently works as a Research Teacher in statistics and probabilistic modeling applied to environmental engineering at AgroParisTech. He greatly contributed to the diffusion of good Bayesian practices in engineering through the numerous applied researches he conducted.; Jacques Bernier est un ancien ingénieur EDF et il fut un pionnier de l'enseignement de la décision statistique à l'ISUP. Je témoigne de la qualité de son enseignement que j'ai jadis suivi avec plaisir. Depuis son départ à la retraite en 1991, Jacques Bernier continue à être très actif scientifiquement et à publier des articles de recherche en statistique bayésienne appliquée. Il est l'un des scientifiques qui aura le plus contribué à la diffusion et à la démonstration du potentiel de l'approche bayésienne en hydrologie. Son compère et disciple, Éric Parent, est ingénieur des Ponts, des Eaux et des Forêts. Il travaille aujourd'hui comme enseignant-chercheur en statistiques appliquées et en modélisation probabiliste pour l'ingénierie environnementale à AgroParisTech. Il a fait énormément pour la pénétration de bonnes pratiques bayésiennes en ingéniérie par les nombreuses recherches appliquées qu'il orchestre.

In Québec (Canada), the donation deferral for men who have sex with men (MSM) has recently been shortened to 3 months. Whether this change impacted compliance with pre-donation screening is unknown. We assessed compliance with the disclosure of male-to-male sex and other behavioural risk factors for HIV amid this change.Québec residents who donated from 14 July 2020 to 30 November 2020 were invited to participate in an online survey. Donors were informed that the survey was optional and anonymous. Survey questions were those used for routine pre-donation screening. Rates of reported non-compliance were weighted based on several characteristics.Of 21,918 contacted donors, 7113 (32.45%) participated. Among male participants (N = 3347), six (0.27% [95% confidence interval (CI) = 0.09%-0.44%]) were not compliant with a 3-month MSM deferral. Among female participants (N = 3766), two (0.06% [95% CI = 0.00%-0.13%]) were not compliant with a 3-month deferral for sex with a man who had male-to-male sex ≤12 months. Other risk factors exhibited similar or lower rates of reported non-compliance.Reported non-compliance with a 3-month MSM deferral and the disclosure of other HIV behavioural risk factors was low. These results warrant the investigation of behavioural donor risk assessment approaches to further improve the inclusiveness of blood donation.

International audience; Assessment of human exposure to atmospheric metals is a challenge, and mosses seem to be good biomonitors to help this purpose. Lacking roots, they are easy to collect and analyze. However, to our knowledge, no formal comparison was made between cadmium (Cd) measurements in Grimmia mosses and alternative forecasts of atmospheric Cd pollution as those produced by the CHIMERE chemistry transport model. This work aims at studying this link to improve further biomonitoring. We compare 128 Cd measurements in the cemetery mosses of Paris and Lyon metropolitan areas (France) to CHIMERE Cd atmospheric forecasts. The area to consider around the cemetery for the CHIMERE forecasts has been defined by Kendall rank correlations between both information sources—Cd in mosses and CHIMERE Cd forecasts—from different area sizes. Then, we fit linear models to those two data sets including step-by-step different sources of uncertainty. Finally, we calculate moss predictions to compare predictions and measurements in the two cities. The results show an apparent link between the Cd concentrations in mosses and CHIMERE Cd forecasts including in addition the same unique covariate, the moss support (grave or wall), in the two cities. However, this model cannot be directly transposed from region to region because the strength of the link appears to be regional.

International audience; The formulation of variable selection has been widely developed in the Bayesian literature by linking a random binary indicator to each variable. This Bayesian inference has the advantage of stochastically exploring the set of possible sub-models, whatever their dimension. Bayesian selection approaches, appropriate for categorical predictors, are generally beyond the scope of the standard Bayesian selection of regressors in the linear model since all levels of a categorical variable should be jointly handled in the selection procedure. For categorical covariates, new strategies have been developed to detect the effect of grouped covariates rather than the single effect of a quantitative regressor. In this paper, we review three Bayesian selection methods for categorical predictors: Bayesian Group Lasso with Spike and Slab priors, Bayesian Sparse Group Selection and Bayesian Effect Fusion using model-based clustering. The motivation behind this paper is to provide detailed information about the implementation of the three Bayesian selection methods mentioned above, appropriate for categorical predictors, using the JAGS software. Selection performance and sensitivity analysis of the hyperparameters tuning for prior specifications are assessed under various simulated scenarios. JAGS helps user implement these three Bayesian selection methods for more complex model structures such as hierarchical ones with latent layers.

International audience; Capture-mark-recapture techniques are smart non-invasive sampling methods to evaluate the number of individuals in a population. Primarily used in ecology, they also find a much broader scope for investigations in various fields. From a pedagogical standpoint, they nicely illustrate, in a very simple and practical way, many key points of probabilistic reasoning as a rationale essential 1 to statistician-modellers. Starting from an affordable toy experiment that can be easily performed indoors with stickers, beans, a tablespoon and a saladbowl, we show how to deal with the following key points in a simple and interesting way, in the specific context of estimating the unknown size of a population :-the basic ingredients of a problem of inferential statistics, unknowns versus observables ;-the design of a possible probabilistic/stochastic model by assembling several binomial building blocks, as well as the many possible decomposi-tions of the associated likelihood ;-the search for estimators, their theoretical study as well as the comparative study of their mathematical properties using computer simulations ;-the major operational differences between the frequentist and Bayesian statistical approaches, This experiment also illustrates how the everyday work of a statistician-modeller often resembles the one of a police investigator ....; Les méthodes de capture-marquage-recapture sont des méthodes astucieuses d'échantillonnage peu invasives pour évaluer le nombre d'individus dans une population. Utilisées principalement en écologie, elles trouvent aussi des applications de portée bien plus large pour des enquêtes discrètes dans divers domaines. Du point de vue de la pédagogie, elles permettent d'illustrer de façon simple, pratique et vivante de nombreux points clés du raisonnement probabiliste indispensables au statisticien-modélisateur. A l'aide d'une expérience ludique facile à effectuer en salle avec des gommettes, des haricots secs, une cuillère à soupe et un saladier, nous montrons comment aborder de façon simple et intéressante les points-clés suivants dans le cadre d'un problème d'estimation de la taille inconnue d'une population :-les ingrédients de base du problème de statistique inférentielle considéré, en particulier, inconnues versus observables ;-la construction d'un modèle probabiliste/stochastique possible, fondé sur l'assemblage de plusieurs briques binomiales élémentaires, ainsi que les différentes décompositions possibles de la vraisemblance associée ;-la recherche d'estimateurs, leur étude théorique ainsi que la comparaison de leurs propriétés mathématiques par simulation numérique ;-les différences opérationnelles majeures entre approches statistiques fré-quentielle et bayésienne. Cette expérience permet également d'illustrer en quoi le travail d'un statisticien-modélisateur ressemble bien souvent à celui d'un enquêteur de police....

Le zonage des risques en montagne reste pense comme une procedure normative issue de la transposition du « modele inondation ». Au cœur de ce schema figure le phenomene centennal, reference probabiliste d'une definition problematique, inadaptee a des phenomenes destructeurs, et peu interpretable en termes d'exposition. Ces insuffisances sont sources d'incomprehensions, et elle rend necessaire des raccourcis et des pratiques de terrain securitaires. Cet article propose un changement de paradigme. Le zonage y est envisage comme la un compromis entre les pertes dues au phenomene dommageable et les restrictions que la societe s'impose. L'etat des connaissances scientifiques ne permet pour l'instant pas de definir une procedure directive complete qu'il ne revient de toute facon pas a la sphere technique d'enoncer. En revanche, cartographier le risque individuel en combinant modele d'alea et susceptibilite au dommages pour differents types d'enjeux puis definir le zonage sur la base de seuils d'acceptabilite permet d'ores et deja d'integrer le caractere multivarie de l'alea, de prendre en compte les incertitudes et de tracer l'ensemble de la procedure de decision. Le choix des seuils de risque individuel constituant les limites de zones et l'affichage du risque residuel apres zonage materialisent le compromis choisi, permettant une reappropriation de la question par la societe. Le cadre generique propose est compatible avec une large gamme de solutions techniques comme d'orientations institutionnelles. In fine des recommandations concretes pour la pratique de meme que des pistes de recherche futures sont formulees. L'ensemble est illustre par un cas d'etude detaille issu du domaine des avalanches, mais la reflexion est transferable a l'ensemble des aleas gravitaires rapides recurrents.

AMS subject classifications. 62K99, 62L05, 60G15; Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs, called control variables, reproduce physical conditions, whereas other inputs, called parameters, are specific to the computer code and most often uncertain. The goal of statistical calibration consists in reducing their uncertainty with the help of a statistical model which links the code outputs with the field measurements. In a Bayesian setting, the posterior distribution of these parameters is typically sampled using Markov Chain Monte Carlo methods. However, they are impractical when the code runs are highly time-consuming. A way to circumvent this issue consists of replacing the computer code with a Gaussian process emulator, then sampling a surrogate posterior distribution based on it. Doing so, calibration is subject to an error which strongly depends on the numerical design of experiments used to fit the emulator. Under the assumption that there is no code discrepancy, we aim to reduce this error by constructing a sequential design by means of the expected improvement criterion. Numerical illustrations in several dimensions assess the efficiency of such sequential strategies.

Meteorological ensemble members are a collection of scenarios for future weather issued by a meteorological center. Such ensembles nowadays form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess point-wise estimate. Unfortunately, ensemble members cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to re-calibrate the ensemble. Two main families of post-processing methods, either competing such as the BMA or collaborative such as the EMOS, can be found in the literature. This paper proposes a mixed-effect model belonging to the collaborative family. The structure of the model is formally justified by Bruno de Finetti’s representation theorem which shows how to construct operational statistical models of ensemble based on judgments of invariance under the relabeling of the members. Its interesting specificities are as follows: (1) exchangeability contributes to parsimony, with an interpretation of the latent pivot of the ensemble in terms of a statistical synthesis of the essential meteorological features of the ensemble members, (2) a multiensemble implementation is straightforward, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto normal statistical structures, first with a direct application for temperatures, then with its very convenient Tobit extension for precipitation. Inference is performed by expectation maximization (EM) algorithms with both steps leading to explicit analytic expressions in the Gaussian temperature case, and recourse is made to stochastic conditional simulations in the zero-inflated precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation ensemble forecasts produced for lead times from 1 to 9 days over five river basins managed by Hydro-Quebec, which ranks among the world’s largest electric companies. These ensemble forecasts, provided by three meteorological global forecast centers (Canadian, USA and European), were extracted from the THORPEX Interactive Grand Global Ensemble (TIGGE) database. The results indicate that post-processed ensembles are calibrated and generally sharper than the raw ensembles for the five watersheds under study. Supplementary materials accompanying this paper appear on-line.

Probabilistic forecasting aims at producing a predictive distribution of the quantity of interest instead of a single best guess point-wise estimate. With regard to water flow forecasts, the two main sources of uncertainty stem from unknown future rainfall and temperature (input error, i.e., meteorological uncertainty) and from the inadequacy of the deterministic simulator mimicking the rainfall-runoff (RR) transformation (hydrological uncertainty or RR error). These two sources of uncertainty can be dealt with separately and only the latter will be considered here. Only hydrological uncertainty is at stake when recorded meteorological data (instead of meteorological forecasts) are used as inputs to feed the RR simulator (RRS) for probabilistic predictions. The predictive performance of the RRS may strongly depend on the hydrological regimes: rapid flood variations induce large errors of anticipation but a series of dry events will translate into a much more smoother sequence of river levels due to the easily predictable behavior of the soil reservoir emptying. Consequently, a model with several regimes adapted to different error structures appears as a solution to cope with the issue of unstationary predictive variance. The river regime is modeled as a latent variable, the distribution of which is based on additional outputs of the RRS to be selected. Inference is performed by the EM algorithm with both steps leading to explicit analytic expressions. Asymptotic confidence regions for the estimates are provided within the same EM framework. Model selection is also performed, including the length of the model memory as well as the choice of explanatory variables for the latent regimes. The model is applied to a series of water flow forecasts routinely issued by two hydroelectricity producers in France and in Qu,bec and compared with their present operational forecasting methods.

[Departement_IRSTEA]Eaux [TR1_IRSTEA]RIVAGE; In this paper, we propose a novel approach for generating avalanche hazard maps based on the spatial dependence of avalanche runout altitudes. The right-truncated data are described with a Bayesian hierarchical model in which the spatio-temporal process is assumed to be the sum of independent spatial and temporal terms. Topography is roughly taken into account according to valley altitude and path exposition, and the spatial dependence is modelled with a Matérn covariance function. An application is performed to the Haute-Savoie region, French Alps. A spatial dependence in runout altitudes is identified, and an effective range of about 10 km is inferred. The temporal trend extracted highlights the increase of avalanche runout altitudes from 1955, attributed to both anthropogenic factors and climate warming. In a cross validation scheme, spatial predictions are provided on undocumented paths using kriging equations. All in all, although our model is unable to take into account small topographic features, it is a first-ever approach that produces very encouraging results. It could be enhanced in future work by incorporating a numerical physically-based code into the modelling.

Although modeling complex environmental spatio-temporal processes, separability between time and space effects is often assumed as a first approach, even though it may be unrealistic. Hence, the development of adapted non-separable spatio-temporal models is a challenging issue. In this work, we are interested in modeling avalanche counts over the whole French Alps, a large area that exhibits zones characterized by distinct climatic behaviors. We have at our disposal a data set of 405, 63-year series of avalanche counts, one series for one township. We assume the series can be divided into several spatial clusters presenting specific temporal trends. On the latent layer of a hierarchical negative binomial-lognormal structure, the clusters are characterized by independent temporal evolutions, modeled using smoothing splines. The clusters arise as the result of a multinomial probit regression, with spatial coordinates used as covariates. Inference is performed within the Bayesian hierarchical framework. The number of clusters is assessed using cross validation. The best score is obtained for a three-cluster model, but other configurations also share some evidence. The first cluster is located in the east of the French Alps, whereas the others are located together in the west part of the French Alps. The three contrasted temporal trends corresponding to the three clusters result from regional climate change effects, interacting with a strong altitudinal control and data limitation. The proposed model could be used for analyzing various other climatic and environmental data sets. Copyright (c) 2012 John Wiley & Sons, Ltd.

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked.

1. Assuming that recruitment variation is one of the main sources of fish population and assemblage changes, it is necessary to understand how natural variations in the environment influence 0+ fish abundance. Temperature regimes play an important role in enhancing both spawning activity and survival during early larval fish development. Flow regime variation, which is a powerful source of stream disturbance, is another factor to be taken into account. 2. Responses to these variables need to be assessed using long-term datasets, since standard statistical approaches fail to provide a causal structure or to quantify the different effects. We therefore used a 26-year dataset to evaluate the respective effects of seven derived independent variables describing the effects of temperature and flow regimes on the 0+ juvenile abundance of eight fish species in the River Rhone. 3. A clustering procedure using the Kendall tau rank correlation coefficient was implemented and identified three groups of fish according to their synchronic variations in juvenile abundance; i.e. varying with decreasing juvenile abundance, slightly increasing juvenile abundance and increasing juvenile abundance. These clusters provided the basis for building hierarchical log-Poisson generalized linear models. The Bayesian paradigm gives a reliable framework for model selection, and the best model was determined using the Bayes Factor. 4. The posterior distribution of the regression parameters was coherent with what was expected based on knowledge of the biology of the different species. It indicates that temperature regime drives 0+ juvenile abundance but that flow regime also plays an important regulating role. The models thus detected evidence of the consequences of specific flow events such as larval drift and an increase in available habitat during higher flow discharges. 5. Our study illustrates the advantages of using a hierarchical modelling approach to quantify ecological effects by improving discrimination between the different sources of uncertainty, leading to better precision when estimating regression parameters.

Complex physical systems are increasingly modeled by computer codes which aim at predicting the reality as accurately as possible. During the last decade, code validation has benefited from a large interest within the scientific community because of the requirement to assess the uncertainty affecting the code outputs. Inspiring frompast contributions to this task, a testing procedure is proposed in this paper to decide either a pure code prediction or a discrepancy-corrected one should be used to provide the best approximation of the physical system. In a particular case where the computer code depends on uncertain parameters, this problem of model selection can be carried out in a Bayesian setting. It requires the specification of proper prior distributions that are well known as having a strong impact on the results. Another way consists in specifying non-informative priors. However, they are sometimes improper, which is a major barrier for computing the Bayes factor. A way to overcome this issue is to use the so-called intrinsic Bayes factor (IBF) in order to replace the ill-defined Bayes factor when improper priors are used. For computer codes which depend linearly on their parameters, the computation of the IBF is made easier, thanks to some explicit marginalization. In the paper, we present a special case where the IBF is equal to the standard Bayes factor when the right-Haar prior is specified on the code parameters and the scale of the code discrepancy. On simulated data, the IBF has been computed for several prior distributions. A confounding effect between the code discrepancy and the linear code is pointed out. Finally, the IBF is computed for an industrial computer code used for monitoring power plant production.

The increasing demand on water resources requires better management of the water deficit situation, may it be unusual droughts or yearly recurring low flows. We propose to use alternating non-homogeneous point processes to model the occurrences and durations of water deficits and surplus. The advantage of this approach is that it is a relatively simple way to model complex, dependent and non-stationary phenomena. It can be used as an alternative to developing more intricate physically based models. Furthermore, alternating point processes can be used to generate synthetic data that may reveal useful for analysis purposes. Most importantly, they allow to subsequently quantify risks related to deficit durations. Our methodology, developed for two types of events under non-homogeneous conditions, consists of six steps: identification of event type, choice of point process, choice of intensity function shape, estimation of intensity function parameters, testing model fitness, and sensitivity analysis. Also included are two new models based on the non-homogeneous Poisson conditional process that take into account external variables such as precipitation and temperatures. We begin with a classification of some point processes and their relation to each other. We describe the procedure for using the pertinent statistical tests. We present our modeling results for 10 Canadian rivers where we observed that in most cases, the simpler point processes were quite adequate.

To fit a lognormal distribution to a complex set of microbial data, including detection data (e.g. presence or absence in 25 g) and enumeration data (e.g. 30 cfu/g), we compared two models: a model called M CLD based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. 1 cfu/25 g) versus a model called M RD that directly uses raw data (presence/absence in test portions, and plate colony counts). We used these two models to simulated data sets, under standard conditions (limit of detection (LOD) = 1 cfu/25 g; limit of quantification (LOQ) = 10 cfu/g) and used a maximum likelihood estimation method (directly for the model M CLD and via the Expectation–Maximisation (EM) algorithm for the model M RD . The comparison suggests that in most cases estimates provided by the proposed model M RD are similar to those obtained by model M CLD accounting for censorship. Nevertheless, in some cases, the proposed model M RD leads to less biased and more precise estimates than model M CLD .

In the context of risk analysis under uncertainty, we focus here on the problem of estimating a so-called quantity of interest of an uncertainty analysis problem, i.e. a given feature of the probability distribution function (pdf) of the output of a deterministic model with uncertain inputs. We will stay here in a fully probabilistic setting. A common problem is how to account for epistemic uncertainty tainting the parameter of the probability distribution of the inputs. In the standard practice, this uncertainty is often neglected (plug-in approach). When a specific uncertainty assessment is made, under the basis of the available information (expertise and/or data), a common solution consists in marginalizing the joint distribution of both observable inputs and parameters of the probabilistic model (i.e. computing the predictive pdf of the inputs), then propagating it through the deterministic model. We will reinterpret this approach in the light of Bayesian decision theory, and will put into evidence that this practice leads the analyst to adopt implicitly a specific loss function which may be inappropriate for the problem under investigation, and suboptimal from a decisional perspective. These concepts are illustrated on a simple numerical example, concerning a case of flood risk assessment.

Standard engineering procedures, such as adopting high return periods as reference events, are a simplified means of handling the complex and multivariate nature of snow avalanches. Furthermore, such methods do not explicitly take into account the elements at risk and/or possible budgetary constraints. In recent years, many authors from a variety of fields have tried to overcome these limitations with quantitative risk evaluations including cost-benefit analyses. Their proposals are based on different modelling assumptions, and often on different definitions for certain important concepts including scenarios, vulnerability relations and time effects. The first goal of this paper is to propose a state of the art, and to discuss the common points, advantages and drawbacks of the various proposals within a unified formal framework based on decision theory. Most of the applications already in use concern long term risk assessment in land use planning and traffic road regulation, but some potential also exists for short term problems including risk assessment to back-country skiing. In a second time, new extensions of a simple decisional model for the optimal design of an avalanche dam are proposed to illustrate the key point of the place of uncertainty in risk analyses. Finally, to stimulate further research efforts, other important outlooks including computational issues, multivariate optimal design and measures of risk alternative to the standard expected loss minimisation are discussed. (C) 2012 Elsevier B.V. rights reserved.

Qui dit modeles realistes, dit aussi difficultes calculatoires. Le but de ce quatrieme chapitre est de donner un apercu des principales familles de methodes d’approximation des distributions a posteriori Dans le cas tres particulier ou le prior est non informatif et que la taille de l’echantillon est grande, la densite a posteriori peut etre approchee par une loi normale multidimensionnelle. Cette approximation asymptotique repose sur les proprietes des estimateurs du maximum de vraisemblance (section 4.2). A l’ere des ordinateurs personnels puissants, cette approximation — fondee sur des hypotheses assez restrictives — est avantageusement abandonnee au profit des methodes numeriques stochastiques. Ce sont d’abord les methodes de Monte-Carlo par chaines de Markov (MCMC). Ces techniques de simulation avec dependance sont presentees en section 4.3, notamment l’algorithme general de Metropolis-Hasting s et lechantillonnage de Gibbs. Ces deux algorithmes sont d’ailleurs implantes dans le logiciel WinBUGS. Les techniques classiques de simulation avec independance ou methodes de Monte-Carlo (MC), issues de lechantillonnage pondere, avec ou sans re-echantillonnage, ont eu plus recemment des developpements importants sous le nom generique de methodes des particules (section 4.4).

Voici un modele bayesien hierarchique (MBH) pour l’analyse des donnees de capture-marquage-recapture de saumons. Ce chapitre se presente comme une suite au chapitre 8 et s’appuie sur l’etude (Rivot et Prevost, 2002). Chaque annee i, ces deux chercheurs de l’INRA de Rennes veulent estimer le nombre inconnu V i de saumons qui remontent la riviere Oir pour frayer ainsi que la probabilite de capture θi du piege utilise pour effectuer ces mesures. Ils disposent d’une serie d’observations allant de 1984 a 2000 collectees sur le terrain par les techniciens de la station experimentale du Moulin des Princes, Nicolas Jeannot et Francois Burban, aides de Jean-Yves Moelo. Pour analyser de telles donnees, on peut vouloir, en premier lieu, faire l’hypothese d’independance complete entre les annees, c’est-a-dire imaginer que les resultats des experiences de capture-marquage-recapture d’une annee ne nous amenent aucune information quant aux resultats possibles des autres annees. A l’oppose, on peut etre tente d’ignorer la variabilite entre chaque annee en regroupant en un meme echantillon les donnees de toutes les annees comme si elles provenaient du meme modele d’observation. Le modele hierarchique realise un compromis astucieux entre ces points de vue extremes. Il suppose que les annees ne sont ni completement identiques ni completement independantes et considere que les θi et les ν i sont issus d’une meme distribution de probabilite dont les parametres sont inconnus.

Parmi tous les problemes d’actualite, ceux qui ont trait a l’exploitation de l’environnement naturel permettent de mesurer, mieux que tout autre, la necessite de s’adapter aux changements climatiques. Ainsi, l’agriculteur en zone sahelienne comme le producteur d’hydroelectricite au Quebec ont grand interet a detecter les changements de regime dans les series chronologiques disponibles. En effet, s’il est indeniable que la prevision du futur repose sur la connaissance du passe, on comprend aisement qu’une telle prevision se refere essentiellement aux informations recueillies depuis que le systeme est reste dans le meme regime stationnaire jusqu’a son etat actuel qui persistera. C’est pourquoi, la detection des changements de regime dans les series chronologiques constitue un theme de recherche tres important pour l’aide a la decision. Se pose alors immediatement la question des transitions. Sont-elles brutales ou ont-elles une duree significative par rapport a l’unite de temps?

Hierarchical Bayesian Modelling is powerful however under-used to model and evaluate the risks associated with the development of pathogens in food industry, to predict exotic invasions, species extinctions and development of emerging diseases, or to assess chemical risks. Modelling population dynamics of Saccharomyces cerevisiae considering its biodiversity and other sources of variability is crucial for selecting strains meeting industrial needs. Using this approach, we studied the population dynamics of S. cerevisiae, the domesticated yeast. widely encountered in food industry, notably in brewery, vinery, bakery and distillery. We relied on a logistic equation to estimate the key variables of population growth, but we took also into account factors able to affect them, namely environmental effects, genetic diversity and measurement errors. Our probabilistic approach allowed us: (i) to model the dynamical behaviour of strains in a given condition under some uncertainty, (ii) to measure environmental effects and (iii) to evaluate genetic variability of the growth key variables.

Dans un contexte decisionnel, la modelisation des valeurs extremes est du plus grand interet puisqu’une protection qui fonctionne pour des evenements extremes pare aussi des evenements de moindre ampleur. Ainsi, la determination de la hauteur d’une digue prend en compte les crues extremes du cours d’eau, y compris celles qui n’ont jamais ete observees. A l’exclusion notable des distributions discretes (processus de comptage), la theorie des valeurs extremes considere un η-echantillon iid et s’interroge sur la distribution de la plus grande ou de la plus petite valeur de cet echantillon lorsque sa taille tend vers l’infini. L’article fondateur implique l’un des plus grands statisticiens classiques (Fisher et Tippett, 1928) dont les travaux furent valides et completes par d’autres personnalites (Gnedenko, 1943), (Jenkinson, 1955). Cependant, certains s’interrogent encore sur le sens meme du concept de probabilite quand on l’applique a des evenements exceptionnels (Bouleau, 1991). Effectivement, le frequentisme radical est, ici, a bout de souffle. Dans ce meme contexte, le paradigme bayesien trouve une nouvelle justification. Ce domaine de la recherche est en plein essor, notamment pour prendre en compte les dependances spatiales et/ou temporelles entre les valeurs extremes (Drees, 2008). Dans ce chapitre d’introduction, nous nous limiterons au cas ou il est raisonnable de postuler l’independance entre les extremes. Cette hypothese fonde les modeles GEV (generalized extremes values) et POT (peak over threshold), modeles qui sont en fait deux expressions differentes d’une meme realite.

On appelle expertise le savoir deja connu en dehors des informations apportees par les resultats experimentaux. Les experts detiennent ce savoir en tout ou en partie. Le modelisateur veut utiliser ce savoir pour construire une distribution a priori sur les parametres du modele de connaissance en main. Parce qu’ils sont experts, on s’attend a ce que ces gens chevronnes parient volontiers sur les memes plages de valeurs. Reconnaitre la qualification de l’expert, c’est prendre acte que ces paris ne sont pas arbitraires et des methodes ont ete developpees pour les traduire du mieux possible sous la forme d’une distribution de probabilite. Dans ce chapitre, nous en exposons quelques-unes.

Une tâche recurrente de l’activite scientifique est d’expliquer le comportement d’une variable endogene ou reponse a partir de variables exogenes ou stimuli. Le modele de regression lineaire est certainement le plus utilise, pas toujours a bon escient. Le modele lineaire generalise, moins gourmand en hypotheses que le modele lineaire, postule que la reponse est un membre de la famille exponentielle des distributions statistiques a deux parametres. Le modele de regression logistique est certainement le plus connu. Nous l’appliquerons a une enquete menee aupres de 68 prothesistes dentaires appartenant a 10 entreprises differentes du Grand-Duche de Luxembourg (Marion, 2007). Nous terminerons avec le modele de Finney qui exploite la regression logistique pour evaluer les performances de melange d’insecticides (Finney, 1971).

L’homme est curieux et c’est sans doute ce qui explique le mieux son cheminement depuis le debut de l’humanite jusqu’a nos jours. Ce besoin de comprendre les phenomenes observes et le desir de les anticiper est au cœur de ses preoccupations. C’est ce qui explique l'emergence et le succes de la statistique, une discipline scientifique en plein essor. Pour definir son objet, on ne saurait mieux faire que Christian Robert (Robert, 2006): „ L’objet principal de la statistique est de mener, grâce a l’observation d’un phenomene aleatoire, une inference sur la distribution probabiliste a l’origine de ce phenomene c’est-a-dire de fournir une analyse (ou une description) d’un phenomene passe, ou une prediction d’un phenomene a venir de nature similaire “.

Les modeles graphiques associent la theorie des graphes, qui modelise des reseaux, a la theorie des probabilites, qui quantifie l’incertitude. L’idee fondamentale est la modularite: un modele complexe est construit en combinant des modeles simples. Les modeles graphiques eclairent parfaitement la notion d’independance conditionnelle. Le modele dit de capture-marquage-recapture constitue un exemple pedagogique d’autant plus interessant qu’il recoit de nombreuses applications pratiques dans les sciences naturelles et humaines.

La modelisation statistique bayesienne revient a imaginer un modele probabiliste, susceptible de reproduire les observations (chap. 1), souvent pour fournir une aide a la decision en avenir incertain (chap. 2). Ce modele est avantageusement represente par un DAG (chap. 3). D’un point de vue operationnel, il faut eliciter le prior (chap. 7) et inferer ses parametres par application de la regle de Bayes (chap. 1). La determination des distributions a posteriori peut necessiter un recours aux methodes de Monte-Carlo (chap. 4). C’est notamment le cas pour les modeles realistes, lesquels impliquent souvent des variables latentes (chap. 3). Leur DAG montre une structure hierarchique et modulaire. Cette modularite confere une grande souplesse au modele comme le montre ce chapitre dedie a l’evaluation des stocks de saumons.

A parsimonious model is presented as an alternative to delta approaches to modelling zero-inflated continuous data. The data model relies on an exponentially compound Poisson process, also called the law of leaks (LOL). It represents the process of sampling resources that are spatially distributed as Poisson distributed patches, each containing a certain quantity of biomass drawn from an exponential distribution. In an application of the LOL, two latent structures are proposed to account for spatial dependencies between zero values at different scales within a hierarchical Bayesian framework. The LOL is compared to the delta-gamma (Delta I") distribution using bottom-trawl survey data. Results of this case study emphasize that the LOL provides slightly better fits to learning samples with a very high proportion of zero values and small strictly positive abundance data. Additionally, it offers better predictions of validation samples.

Sous ce titre quelque peu humoristique, nous nous interessons a un probleme generique qui a de nombreuses applications pratiques: connaissant le rang d’un element d’un ensemble fini ordonne E, on se propose d’inferer le nombre d’elements de E. En fait, c’est la generalisation de ce probleme a une collection d’ensembles finis ordonnes qui nous interesse. Sous le paradigme bayesien, le recours aux variables latentes (voir chap 3, p. 3.2.3) permet d’introduire un second niveau de variation entre les ensembles, ce qui confere au modele une structure hierarchique. Mais un modele n’est utile que s’il est calculable et c’est pourquoi les modeles hierarchiques et les methodes de Monte-Carlo sont indissociables.

Based on a previous township-scale model, a spatio-temporal framework is proposed to study the fluctuations of avalanche occurrence possibly resulting from climate change. The regional annual component is isolated from the total variability using a two-factor nonlinear analysis of variance. Moreover, relying on a Conditional AutoRegressive sub-model for the spatial effects, the structured time trend is distinguished from the random noise with different time series sub-models including autocorrelative, periodic and change-point models. The hierarchical structure obtained takes into account the uncertainty related to the estimation of the annual component for the quantification of the time trend. Bayesian inference is performed using Monte Carlo simulations. This allows a comparison of the different time series models and the prediction of future activity in an explicit unsteady context. Application to the northern French Alps illustrates the information provided by the model's different components, mainly the spatial and temporal terms as well as the spatio-temporal fluctuation of the relative risk. For instance, it shows no strong modifications in mean avalanche activity or in the number of winters of low or high activity over the last 60 years. This suggests that climate change has recently had little impact on the avalanching rhythm in this region. However, significant temporal patterns are highlighted: a complex combination of abrupt changes and pseudo-periodic cycles of approximately 15 years. For anticipating the future response of snow avalanches to climate change, correlating them with fluctuations of the constraining climatic factors is now necessary.

Ce chapitre traite d’une pollution particulierement pernicieuse, la pollution a l’interieur des habitations par les materiaux emetteurs couramment utilises dans la fabrication des objets usuels. Cette pollution peut constituer une menace pour la sante. Par consequent, determiner le temps d’activite d’un emetteur de polluants est utile, notamment pour l’elaboration de normes. Nous traiterons specifiquement le cas des formaldehydes emis par certains tapis et carpettes. Il s’agit d’un phenomene intrinsequement non lineaire et le but est de determiner le temps au bout duquel le materiau emetteur a perdu l’essentiel de son activite. La mesure du taux d’emission est indirecte. On la deduit de la concentration du polluant regulierement mesuree dans une enceinte climatisee et ventilee. En pratique, le dispositif experimental produit peu de donnees. Typiquement, il faut maintenir la ventilation et les conditions experimentales rigoureusement constantes durant une dizaine de jours. On comprend qu’une telle experience n’est pas aisement repetable dans les memes conditions; on peut meme dire qu’elle est unique ! Par consequent, il est essentiel de quantifier les incertitudes sur les parametres qui regissent le taux d’emission, en particulier pour comparer les effets potentiellement nocifs de produits concurrents.

Quand on s’interesse a une experience aleatoire dichotomique, l’hypothese que les observations successives constituent un processus de Bernoulli peut etre justifiee, tantot par la nature de l’experience aleatoire (p. ex. jeu de pile ou face), tantot constituer une hypothese de pure commodite « pour voir ». Dans tous les cas, elle conduit au modele beta-binomial et, quand l’evenement d’interet est rare, au modele gamma-Poisson. Ces modeles, tres simples, nous permettent de construire un probleme fictif d’aide a la decision, fonde sur un drame reel ayant fait la une des journaux: Aurions-nous pu eviter la catastrophe de Montroc?

For snow avalanches, passive defense structures are generally designed by considering high return period events. However, defining a return period turns out to be tricky as soon as different variables are simultaneously considered. This problem can be overcome by maximizing the expected economic benefit of the defense structure, but purely stochastic approaches are not possible for paths with a complex geometry in the runout zone. Therefore, in this paper, we include a multivariate numerical avalanche propagation model within a Bayesian decisional framework. The influence of a vertical dam on an avalanche flow is quantified in terms of local energy dissipation with a simple semi-empirical relation. Costs corresponding to dam construction and the damage to a building situated in the runout zone are roughly evaluated for each dam height-hazard value pair, with damage intensity depending on avalanche velocity. Special attention is given to the poor local information to be taken into account for the decision. Using a case study from the French avalanche database, the Bayesian optimal dam height is shown to be more pessimistic than the classical optimal height because of the increasing effect of parameter uncertainty. It also appears that the lack of local information is especially critical for a building exposed to the most extreme events only. The residual hazard after dam construction is analyzed and the sensitivity to the different modelling assumptions is evaluated. Finally, possible further developments of the approach are discussed.

International audience; For snow avalanches, passive defense structures are generally designed by considering high return period events. However, defining a return period turns out to be tricky as soon as different variables are simultaneously considered. This problem can be overcome by maximizing the expected economic benefit of the defense structure, but purely stochastic approaches are not possible for paths with a complex geometry in the runout zone. Therefore, in this paper, we include a multivariate numerical avalanche propagation model within a Bayesian decisional framework. The influence of a vertical dam on an avalanche flow is quantified in terms of local energy dissipation with a simple semi-empirical relation. Costs corresponding to dam construction and the damage to a building situated in the runout zone are roughly evaluated for each dam heighthazard value pair, with damage intensity depending on avalanche velocity. Special attention is given to the poor local information to be taken into account for the decision. Using a case study from the French avalanche database, the Bayesian optimal dam height is shown to be more pessimistic than the classical optimal height because of the increasing effect of parameter uncertainty. It also appears that the lack of local information is especially critical for a building exposed to the most extreme events only. The residual hazard after dam construction is analyzed and the sensitivity to the different modelling assumptions is evaluated. Finally, possible further developments of the approach are discussed.