Identifying intrinsic variability in multivariate systems through linearized inverse methods

Celeux, Gilles; Grimaud, Agnès; Lefebvre, Yannick; Rocquigny, Etienne de

doi:10.1080/17415971003624330

Cited by 20 publications

(14 citation statements)

References 6 publications

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“…A linearised method In order to limit to a reasonable amount of computation the number of calls to the function H to estimate the model parameters, a linear approximation of the model defined in (1) has been investigated in Celeux et al (2009). In this approach the function H is linearised around a fixed value x 0 (chosen from expert informations).…”

Section: The Model and Its Linear Identificationmentioning

confidence: 99%

“…In the following, for simplicity, the variance matrix R is assumed to be known to sketch the approach of Celeux et al (2009). First the linear model (2) is supposed to be identifiable.…”

Section: The Model and Its Linear Identificationmentioning

confidence: 99%

“…As in Celeux et al (2009), this paper concentrates on the situation where there is an irreducible uncertainty or variability in the input parameters of a physical model. Observations are modelled with a vector of physical variables y that are connected to uncertain inputs x through a deterministic (and supposedly well-known) physical model y = H(x, d).…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organised as follows. In Section 2, the model is stated and the linear procedure of Celeux et al (2009) is summarised. In Section 3, a stochastic procedure using a non linear approximation of H is presented.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, it is desirable or necessary to limit the number of calls to the H function. For this very reason, Celeux et al (2009) investigated efficient estimation algorithms based on a linearisation of the model around a fixed value x 0 to estimate the parameters distributions in this context. But, the linearisation method has some drawbacks associated to the approximation error induced, and the potential difficulty in choosing an adequate linearisation point before identification.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear methods for inverse statistical problems

Barbillon

Celeux

Grimaud

et al. 2011

Computational Statistics & Data Analysis

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In the uncertainty treatment framework considered in this paper, 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 to a reasonable level the number of (usually burdensome) physical model runs inside the inversion algorithm, a non linear approximation methodology making use of Kriging and 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 non linear approach is to be preferred to linearisation are highlighted. Key-words:Uncertainty

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Section: The Model and Its Linear Identificationmentioning

confidence: 99%

“…In the following, for simplicity, the variance matrix R is assumed to be known to sketch the approach of Celeux et al (2009). First the linear model (2) is supposed to be identifiable.…”

Section: The Model and Its Linear Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear methods for inverse statistical problems

Barbillon

Celeux

Grimaud

et al. 2011

Computational Statistics & Data Analysis

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Combined Model Estimation through Inverse Techniques

Rocquigny

2012

Modelling Under Risk and Uncertainty

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An adaptive kriging method for solving nonlinear inverse statistical problems

Fu¹,

Couplet²,

Bousquet

2017

Environmetrics

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In various environmental contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi)+Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is implemented by a CPU‐consuming computer model H, a major practical difficulty is to perform the statistical inference with a relatively small number of runs of H. A Bayesian statistical framework is considered to make use of possible prior knowledge on the parameters of the distribution of the Xi, which is assumed Gaussian. Moreover, a Markov Chain Monte Carlo algorithm is carried out to estimate their posterior distribution by replacing H by a kriging metamodel build from a limited number of simulated experiments. Two heuristics, involving two different criteria to be optimized, are proposed to sequentially design these computer experiments in the limits of a given computational budget. The first criterion is a weighted integrated mean square error. The second one, called expected conditional divergence, developed in the spirit of the stepwise uncertainty reduction criterion is based on the discrepancy between two consecutive approximations of the target posterior distribution. Several numerical comparisons conducted over a toy example then a motivating hydraulic real case study show that such adaptive designs can significantly outperform the classical choice of a maximin latin hypercube design of experiments. Dealing with a major concern in hydraulic engineering, a particular emphasis is placed upon the prior elicitation of the case study, highlighting the overall feasibility of the methodology. Faster convergences and manageability considerations lead to recommend the use of the expected conditional divergence criterion in practical applications.

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Identifying intrinsic variability in multivariate systems through linearized inverse methods

Cited by 20 publications

References 6 publications

Nonlinear methods for inverse statistical problems

Nonlinear methods for inverse statistical problems

Combined Model Estimation through Inverse Techniques

An adaptive kriging method for solving nonlinear inverse statistical problems

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