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    Bayesian Optimal Experimental Design Using Multilevel Monte Carlo

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    Type
    Poster
    Authors
    Ben Issaid, Chaouki cc
    Long, Quan cc
    Scavino, Marco cc
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2015-01-07
    Permanent link to this record
    http://hdl.handle.net/10754/624067
    
    Metadata
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    Abstract
    Experimental design is very important since experiments are often resource-exhaustive and time-consuming. We carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions. Optimizing this utility function enables us to design experiments that yield the most informative data for our purpose. One of the major difficulties in evaluating the expected information gain is that the integral is nested and can be high dimensional. We propose using Multilevel Monte Carlo techniques to accelerate the computation of the nested high dimensional integral. The advantages are twofold. First, the Multilevel Monte Carlo can significantly reduce the cost of the nested integral for a given tolerance, by using an optimal sample distribution among different sample averages of the inner integrals. Second, the Multilevel Monte Carlo method imposes less assumptions, such as the concentration of measures, required by Laplace method. We test our Multilevel Monte Carlo technique using a numerical example on the design of sensor deployment for a Darcy flow problem governed by one dimensional Laplace equation. We also compare the performance of the Multilevel Monte Carlo, Laplace approximation and direct double loop Monte Carlo.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
    Collections
    Posters; Applied Mathematics and Computational Science Program; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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