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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.

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.

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.

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.

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.

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.