New Fréchet features for random distributions and associated sensitivity indices

In this article we define new Fréchet features for random cumulative distribution functions using contrast. These contrasts allow to construct Wasserstein costs and our new features minimize the average costs as the Fréchet mean minimizes the mean square Wasserstein2 distance. An example of new features is the median, and more generally the quantiles. From these definitions, we are able to define sensitivity indices when the random distribution is the output of a stochastic code. Associated to the Fréchet mean we extend the Sobol indices, and in general the indices associated to a contrast that we previously proposed

New sensitivity analysis subordinated to a contrast

International audienceIn a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this parameter of interest. The aim of this paper is to define {\it goal oriented sensitivity indices} and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution $Y$. We name the framework we present as {\it Goal Oriented Sensitivity Analysis} (GOSA)

Stochastic inverse problem with noisy simulator - Application to aeronautical model

International audienceInverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial aircraft, where we only consider the Cruise phase . From a data base of fuel mass consumptions during the cruise phase, we aim at identifying the Speci c Fuel Consumption (SFC) in a robust way, given the uncertainty of the cruise speed V and the lift-to-drag ratio F. In this paper, we present an estimation procedure based on Maximum-Likelihood estimation, taking into account this uncertainty

Risk bounds for new M-estimation problems

International audienceIn this paper, we develop new algorithms for parameter estimation in the case of models type Input/Output in order to represent and to characterize a phenomenon Y. From experimental data Y_{1},...,Y_{n} supposed to be i.i.d from Y, we prove risk bounds qualifying the proposed procedures in terms of the number of experimental data n, computing budget m and model complexity. The methods we present are general enough which should cover a wide range of applications