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    Fast Estimation of Expected Information Gain for Bayesian Experimental Design Based on Laplace Approximation

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    Type
    Poster
    Authors
    Long, Quan cc
    Scavino, Marco cc
    Tempone, Raul cc
    Wang, Suojin
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-01-06
    Permanent link to this record
    http://hdl.handle.net/10754/623976
    
    Metadata
    Show full item record
    Abstract
    Shannon-type expected information gain is an important utility in evaluating the usefulness of a proposed experiment that involves uncertainty. Its estimation, however, cannot rely solely on Monte Carlo sampling methods, that are generally too computationally expensive for realistic physical models, especially for those involving the solution of stochastic partial differential equations. In this work we present a new methodology, based on the Laplace approximation of the posterior probability density function, to accelerate the estimation of expected information gain in the model parameters and predictive quantities of interest. Furthermore, in order to deal with the issue of dimensionality in a complex problem, we use sparse quadratures for the integration over the prior. We show the accuracy and efficiency of the proposed method via several nonlinear numerical examples, including a single parameter design of one dimensional cubic polynomial function and the current pattern for impedance tomography.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
    Collections
    Posters; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

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