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

Statistical Analysis and Parameter Selection for Mapper

In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a method to automatically tune its parameters and compute confidence regions on its topological features, such as its loops and flares. This allows to circumvent the issue of testing a large grid of parameters and keeping the most stable ones in the brute-force setting, which is widely used in visualization, clustering and feature selection with the Mapper.Comment: Minor modification

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

Some conjectures on the two main power indices

The purpose of this paper is to present a structural specification of the Shapley- Shubik and Banzhaf power indices in a weighted voting rule. We compare them in term of the cardinality of the sets of power vectors (PV). This is done in different situations where the quota or the number of seats are fixed or not.Shapley-Shubik, Banzhaf, power index, power vectors.

The role of relational competence in the health care sector

International audienceThe role of entrepreneurs is highly regarded in our societies. It is widely recognized that their roles are not limited to the private sector, but can affect all sectors of the economy. In view of this, we focus on entrepreneurs acting in the healthcare sector. We concentrate more particularly on these entrepreneurs' specific competences. We propose to conceptualise the concept of relational competence, defined as the act of building and structuring relationships in order to adapt and innovate in a given environment. The aim of this exploratory study is to better understand why this type of competence is expected on the construction site of a new hospital in France