Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.Comment: 21 pages, 6 figure

Maximin design on non hypercube domain and kernel interpolation

In the paradigm of computer experiments, the choice of an experimental design is an important issue. When no information is available about the black-box function to be approximated, an exploratory design have to be used. In this context, two dispersion criteria are usually considered: the minimax and the maximin ones. In the case of a hypercube domain, a standard strategy consists of taking the maximin design within the class of Latin hypercube designs. However, in a non hypercube context, it does not make sense to use the Latin hypercube strategy. Moreover, whatever the design is, the black-box function is typically approximated thanks to kernel interpolation. Here, we first provide a theoretical justification to the maximin criterion with respect to kernel interpolations. Then, we propose simulated annealing algorithms to determine maximin designs in any bounded connected domain. We prove the convergence of the different schemes.Comment: 3 figure

Approximate Bayesian Computational methods

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study the various improvements and extensions made to the original ABC algorithm over the recent years.Comment: 7 figure

Sciences et société en interaction sur Internet. Éléments pour une histoire de l'édition électronique en sciences humaines et sociales

doi:10.4074/S0336150009001100The rise of digital networks is a critical time in the complicated history of the relationship between science and society, both in terms of technological development and its impact on scientific communication. The example of humanities and social science highlights their mediating role in the relationship between science and society.Dans l'histoire des rapports complexes qu'entretiennent sciences et société, le développement des réseaux numériques constitue un moment stratégique, que ce soit au niveau de leur développement technique, ou des modifications que ce développement produit sur les formes de la communication scientifique. Le cas particulier des sciences humaines et sociales met bien en évidence le rôle de médiation que les TIC jouent dans les relations entre sciences et société

Humanités numériques: État des lieux et positionnement de la recherche française dans le contexte international

Si, voici quelques années, il pouvait paraître étrange d'associer le numérique aux humanités, le monde scientifique voit aujourd'hui collaborer informaticiens et sociologues, ingénieurs et spécialistes de littérature. Ces alliances inédites renouvellent profondément les formes, les rythmes et la circulation des sciences humaines. Comprendre une révolution scientifiqueFaire le point sur cette mutation en cours, mesurer la part que peut y prendre la recherche française : tel est le double enjeu de l'étude sur les Humanités numériques aujourd'hui publiée par l'Institut français. Réalisée par Marin Dacos et Pierre Mounier, animateurs du Centre pour l'édition électronique ouverte (acteur majeur en France dans ce domaine à travers le portail Open Edition, palette d'instruments bien connue des chercheurs), Humanités numériques – État des lieux et positionnement de la recherche française dans le contexte international trace les contours d'un champ en pleine expansion. Qu'il s'agisse de publier en ligne de vastes fonds d'archives, d'analyser en direct l'impact des réseaux sociaux sur les mobilisations militantes ou de mettre au travail une communauté d'internautes sur des pans entiers du patrimoine culturel, le tournant numérique concerne aujourd'hui tous les secteurs de la recherche sur la société, les œuvres et la culture : l'étude ici publiée éclaire de manière précise et accessible cette transformation globale

Efficient learning in ABC algorithms

Approximate Bayesian Computation has been successfully used in population genetics to bypass the calculation of the likelihood. These methods provide accurate estimates of the posterior distribution by comparing the observed dataset to a sample of datasets simulated from the model. Although parallelization is easily achieved, computation times for ensuring a suitable approximation quality of the posterior distribution are still high. To alleviate the computational burden, we propose an adaptive, sequential algorithm that runs faster than other ABC algorithms but maintains accuracy of the approximation. This proposal relies on the sequential Monte Carlo sampler of Del Moral et al. (2012) but is calibrated to reduce the number of simulations from the model. The paper concludes with numerical experiments on a toy example and on a population genetic study of Apis mellifera, where our algorithm was shown to be faster than traditional ABC schemes

Universality of Tip Singularity Formation in Freezing Water Drops

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with observations.Comment: Letter format, 5 pages, 3 figures. Note: authors AGM and ORE contributed equally to the pape