Global sensitivity analysis of computer models with functional inputs

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation

Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables gives always the same output value). This paper proposes a global sensitivity analysis methodology for stochastic computer code (having a variability induced by some uncontrollable variables). The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, non parametric joint models (based on Generalized Additive Models and Gaussian processes) are discussed. The relevance of these new models is analyzed in terms of the obtained variance-based sensitivity indices with two case studies. Results show that the joint modeling approach leads accurate sensitivity index estimations even when clear heteroscedasticity is present

Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of the usual maximum likelihood estimator, Bayesian inference based on composite likelihoods has yet to be explored. In this paper we investigate the use of the Metropolis--Hastings algorithm to compute a pseudo-posterior distribution based on the composite likelihood. Two methodologies for adjusting the algorithm are presented and their performance on approximating the true posterior distribution is investigated using simulated data sets and real data on spatial extremes of rainfall

Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes

Consolidation de l'information hydrologique disponible localement et régionalement pour l'estimation probabiliste du régime des crues.

Le praticien, lors de l'étape de prédétermination des débits de crue, est souvent confronté à un jeu de données restreint. Dans notre travail de recherche, nous avons proposé trois nouveaux modèles probabilistes spécialement conçus pour l'estimation des caractéristiques du régime des crues en contexte partiellement jaugé. Parmi ces modèles, deux d'entre eux sont des modèles dits régionaux, i.e. intégrant de l'information en provenance de stations ayant un comportement réputé similaire à celui du site étudié. Ces modèles, basés sur la théorie Bayésienne, ont montré une grande robustesse au degré d'hétérogénéité des sites appartenant à la région. De même, il est apparu que pour l'estimation des forts quantiles (T ≥ 50 ans), l'idée d'un paramètre régional contrôlant l'extrapolation est pertinente mais doit d'être intégrée de manière souple et non imposée au sein de la vraisemblance. L'information la plus précieuse dont le praticien dispose étant celle en provenance du site d'étude, le troisième modèle proposé revient sur l'estimation à partir des seules données contemporaines au site d'étude. Ce nouveau modèle utilise une information plus riche que celle issue d'un échantillonnage classique de v. a. i. id. maximales puisque toute la chronique est exploitée. Dès lors, même avec seulement cinq années d'enregistrement et grâce à une modélisation de la dépendance entres les observations successives, la taille des échantillons exploités est alors bien plus importante. Nous avons montré que pour l'estimation des quantiles de crues, ce modèle surpasse très nettement les approches locales classiquement utilisées en hydrologie. Ce résultat est d'autant plus vrai lorsque les périodes de retour deviennent importantes. Enfin, part construction, cette approche permet également d'obtenir une estimation probabiliste de la dynamique des crues. To define the design flood, practitioners must often deal with only few data available. The aim of this work was to propose new classes of probabilistic models that are more accurate for this kind of applications. In this perspective, we propose three different models: two regional approaches and a fully local one. Unlike fully local models, the regional approaches include information from other gauging stations. Our results show that the proposed regional Bayesian estimators are more robust to the discordancy degree of the sites within the region. In addition, for larger quantile estimation (T ≥ 50 years), the concept of a regional parameter which controls the tail behaviour seems to be relevant. However, this concept has to be proposed and not imposed within the likelihood function. It is overwhelmingly clear that the most important information one disposes is the target site one. To this aim, we propose a third model that is fully local, i.e., which only uses the latest recorded data. This new model is innovative as the whole time series is involved in the estimation procedure; not only c1uster maxima. Consequently, even with only a five years record length time series, the sample size becomes large. Our results show that, for flood quantile estimations, this model c1early outperforms the estimators conventionally used in hydrology. Furthermore, by definition, this model allows inferences on flood dynamics

ABC random forests for Bayesian parameter inference

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.Comment: Main text: 24 pages, 6 figures Supplementary Information: 14 pages, 5 figure