Nonlinear methods for inverse statistical problems

• Published in: Computational statistics & data analysis Vol. 55; no. 1; pp. 132 - 142
• Main Authors: Barbillon, Pierre, Celeux, Gilles, Grimaud, Agnès, Lefebvre, Yannick, De Rocquigny, Étienne
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Algorithms; Approximation; Dykes; Exact sciences and technology; General topics; Kriging; Mathematical analysis; Mathematical models; Mathematics; Multivariate analysis; Nonlinear approximation; Nonlinearity; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Samples; Sciences and techniques of general use; Statistical methods; Statistics; Stochastic algorithm; Uncertainty modelling; Uncertainty modelling Nonlinear approximation Kriging Stochastic algorithm; Stochastic algorithm; Uncertainty modelling; Nonlinear approximation; Kriging; Data analysis; Statistical distribution; Sample size; Multivariate distribution; Probability distribution; Nonlinear problems; Multivariate analysis; Inverse problem; Statistical method; Hypothesis test; Statistical test; Numerical analysis; Sampling theory; Statistical computation; Linear approximation; Non linear approximation; Simulation model; Sample survey; EM algorithm
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.05.030

In the uncertainty treatment framework considered, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution–the dispersion of which is independent of the sample size since intrinsic variability is at stake–based on observation of some model outputs. Moreover, in order to limit the number of (usually burdensome) physical model runs inside the inversion algorithm to a reasonable level, a nonlinear approximation methodology making use of Kriging and a stochastic EM algorithm is presented. It is compared with iterated linear approximation on the basis of numerical experiments on simulated data sets coming from a simplified but realistic modelling of a dyke overflow. Situations where this nonlinear approach is to be preferred to linearisation are highlighted.