Nonlinear methods for inverse statistical problems

Barbillon, Pierre; Celeux, Gilles; Grimaud, Agnès; Lefebvre, Yannick; Rocquigny, ítienne De

doi:10.1016/j.csda.2010.05.030

Cited by 18 publications

(10 citation statements)

References 12 publications

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“…Kriging is massively used in global optimization and uncertainty quantification [7] [8,9] [10] [11]. As pointed out in [12], often in practical applications, Kriging is mostly used in its basic configuration known as Ordinary Kriging, because of the lack of a priori knowledge about the main trends of the function of interest.…”

Section: Introductionmentioning

confidence: 99%

Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement

Cortesi

Jannoun²,

Congedo

2019

Journal of Computational Physics

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Polynomials selected by adaptive PDD are used as a sparse basis for Universal Kriging. • Novel strategy to refine the Experimental design based on anisotropic mesh adaptation. • Adding a fixed number of new training points on edges maximizing an error criterion. • Convergence improvements on several algebraic test-cases with respect to the state-of-the-art. • Application on two engineering problems in the aerospace field.

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Section: Introductionmentioning

confidence: 99%

Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement

Cortesi

Jannoun²,

Congedo

2019

Journal of Computational Physics

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“…Celeux et al (2010) considered a maximum likelihood estimation by expectation-conditional maximisation either (Liu & Rubin, 1994) based on an iterative linearisation of H: this algorithm should be avoided if the nonlinearities of H relative to x are significant; otherwise, it can be very efficient. Barbillon, Celeux, Grimaud, Lefebvre, and de Rocquigny (2011) proposed to couple a stochastic expectation maximisation algorithm (Celeux & Diebolt, 1988) with a kriging metamodelling of H to improve the robustness of the estimation.…”

Section: Introductionmentioning

confidence: 99%

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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“…A frequentist technique that is premised on the simulation of an explicitly marginalized likelihood is proposed in [32]. There are also attempts to compute approximate solutions based on variants of the expectation-maximization algorithm within a linearized Gaussian frame [33] or with the aid of Kriging surrogates [34]. A methodological review of this school of probabilistic inversion is found in [35].…”

Section: Introductionmentioning

confidence: 99%