Identifying intrinsic variability in multivariate systems through linearised inverse methods - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2007

Identifying intrinsic variability in multivariate systems through linearised inverse methods

(1) , (1) , (2) , (2)
1
2
Gilles Celeux
  • Function : Author
  • PersonId : 833415
Agnès Grimaud
  • Function : Author
  • PersonId : 832301
Yannick Lefèbvre
  • Function : Author
EDF
Etienne de Rocquigny
  • Function : Author
EDF

Abstract

A growing number of industrial risk studies include some form of treatment of the numerous sources of uncertainties affecting the conclusions; in the uncertainty treatment framework considered in this paper, the intrinsic variability of the uncertainty sources is modelled by a multivariate probability distribution. A key difficulty traditionally encountered at this stage is linked to the highly-limited sampling information directly available on uncertain input variables. A possible solution lies in the integration of indirect information, such as data on other more easily observable parameters linked to the parameters of interest through a well-known physical model. This leads to a probabilistic inverse problem: The objective is to identify a probability distribution, the dispersion of which is independent of the sample size since intrinsic variability is at stake. To limit to a reasonable level the number of (usually large CPU-time consuming) physical model runs inside the inverse algorithms, a linear approximation in a Gaussian framework are investigated in this paper. First a simple criterion is exhibited to ensure the identifiability of the model (i.e. the existence and unicity of a solution to the inverse problem). Then, the solution is computed via EM-type algorithms taking profit of the missing data structure of the estimation problem. The presentation includes a so-called ECME algorithm that can be used to overcome the possible pathology of slow convergence which affects the standard EM algorithm. Numerical experiments on simulated and real data sets highlight the good performances of these algorithms, as well as some precautions to be taken when using this approach.
Fichier principal
Vignette du fichier
RR-6400.pdf (784.08 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00200113 , version 1 (20-12-2007)
inria-00200113 , version 2 (20-12-2007)

Identifiers

  • HAL Id : inria-00200113 , version 2

Cite

Gilles Celeux, Agnès Grimaud, Yannick Lefèbvre, Etienne de Rocquigny. Identifying intrinsic variability in multivariate systems through linearised inverse methods. [Research Report] RR-6400, INRIA. 2007. ⟨inria-00200113v2⟩
210 View
111 Download

Share

Gmail Facebook Twitter LinkedIn More