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Reports (Research Report) Year : 2007

Identifying intrinsic variability in multivariate systems through linearised inverse methods

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Gilles Celeux
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Agnès Grimaud
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Yannick Lefèbvre
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Etienne de Rocquigny
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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.
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Dates and versions

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


  • HAL Id : inria-00200113 , version 2


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⟩
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