@CONFERENCE{PR-CMGC-17-107, author = {De Lozzo, M. and Mycek, P. and Ricci, S. and Rochoux, M. and Roy, P. and Goutal, N. and Ruede, U. }, title = {Méthodes de Monte-Carlo multi-niveaux pour la quantification d’incertitudes et l’assimilation de données – Application à la modélisation fluviale}, year = {2017}, month = {6}, booktitle = {49th Days of Statistics}, address = {Avignon, France}}

@CONFERENCE{PR-CMGC-17-300, author = {Mycek, P. and De Lozzo, M. and Ricci, S. and Rochoux, M. and Roy, P. and Goutal, N. }, title = {Multilevel Monte Carlo estimation of covariances in the context of open-cahenne flow simulation}, year = {2017}, month = {7}, organization = {CEMRACS 17/07-25/08/2017, CIRM, Marseille}}

@TECHREPORT{TR-PA-18-128, author = {Mycek, P. and De Lozzo, M. }, title = {Multilevel Monte Carlo covariance estimation for the computation of Sobol' indices}, year = {2018}, institution = {Cerfacs}, month = {9}, address = {42 avenue Gaspard Coriolis, 31057 Toulouse cedex 1}, type = {Technical report}, abstract = {Crude and quasi Monte Carlo (MC) sampling techniques are common tools dedicated to estimating statistics of a random quantity of interest, e.g. its expectation, variance or covariance. We focus here on the uncertainty quantification framework where the quantity of interest is the output of a numerical simulator fed with uncertain (random) input parameters. Then, sampling the output involves running the simulator for different samples of the inputs, which may be computationally time-consuming. To reduce the cost of sampling, a first approach consists in replacing the numerical simulator by a surrogate model that is cheaper to evaluate, thus making it possible to generate more samples of the output and therefore leading to a lower sampling error. However, this approach adds to the sampling error an unavoidable model error. Another approach, which does not introduce any model error, is the so-called multilevel MC (MLMC) method. Given a sequence of levels corresponding to numerical simulators with increasing accuracy and computational cost, MLMC combines samples obtained at different levels to construct an estimator at a reduced cost compared to standard MC sampling. The number of levels and the sample sizes on each level may be determined by a sequential algorithm driven by a target accuracy. In this paper, we extend theorems of MLMC theory dedicated to expectation and variance estimation to covariance estimation, and we propose a novel version of the multilevel algorithm, driven by a target cost. These results are used in a sensitivity analysis context in order to derive a multilevel estimation of Sobol' indices, whose building blocks can be written as covariance terms in a pick-and-freeze formulation. These theoretical and methodological contributions are successfully tested on an initial value problem with random parameters. }, keywords = {Monte Carlo, Multilevel Monte Carlo, Parameter estimation, Covariance, Uncertainty quantification, Sensitivity analysis, Sobol' indices}, pdf = {https://cerfacs.fr/wp-content/uploads/2018/09/TR-PA-18-128.pdf}}