Multilevel Monte Carlo estimation of expected information gains
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The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest θ is reduced o... as discussed by the authors, and it is defined asAbstract:
The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest θ is reduced o...read more
Citations
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Journal ArticleDOI
Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design
TL;DR: In this article, a multilevel Double Loop Monte Carlo (MLDLMC) is proposed to estimate the expected information gain for Bayesian inference of the fiber orientation in composite laminate materials from an electrical impedance tomography experiment.
Journal ArticleDOI
Optimal Bayesian experimental design for subsurface flow problems
TL;DR: A novel approach for development of polynomial chaos expansion surrogate model for the design utility function by demonstrating how the orthogonality of PCE basis polynomials can be utilized in order to replace the expensive integration over the space of possible observations by direct construction ofPCE approximation for the expected information gain.
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Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs.
TL;DR: An unbiased Monte Carlo estimator is introduced for the gradient of the expected information gain with finite expected squared $\ell_2$-norm and finite expected computational cost per sample.
Posted Content
Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design
TL;DR: Two multilevel methods for estimating a popular criterion known as the expected information gain (EIG) in Bayesian optimal experimental design are proposed, which are a multilesvel strategy with double loop Monte Carlo and a multileVEL double loop stochastic collocation, which performs a high‐dimensional integration on sparse grids.
Journal ArticleDOI
Optimal design of experiments for optimization-based model calibration using Fisher information matrix
Yongsu Jung,Ikjin Lee +1 more
TL;DR: A framework to find the optimal design of experiments satisfying the target information gain for inference of unknown model parameters based on optimization-based model calibration is developed and the expected Fisher information matrix is approximated to quantify the expected information loss for the maximum likelihood estimation (MLE).
References
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Journal ArticleDOI
Bayesian Experimental Design: A Review
TL;DR: This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models, and presents a uniied view of the topic by putting experimental design in a decision theoretic framework.
Journal ArticleDOI
Multilevel Monte Carlo Path Simulation
TL;DR: It is shown that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations.
Journal ArticleDOI
On a Measure of the Information Provided by an Experiment
TL;DR: In this paper, a measure of the information provided by an experiment is introduced, derived from the work of Shannon and involves the knowledge prior to performing the experiment, expressed through a prior probability distribution over the parameter space.
Journal ArticleDOI
Multilevel Monte Carlo methods
TL;DR: A review of the progress in multilevel Monte Carlo path simulation can be found in this article, where the authors highlight the simplicity, flexibility and generality of the multi-level Monte Carlo approach.
Journal ArticleDOI
Simulation-based optimal Bayesian experimental design for nonlinear systems
Xun Huan,Youssef M. Marzouk +1 more
TL;DR: This work proposes a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models, and focuses on finding sets of experiments that provide the most information about targeted sets of parameters.