Multilevel Monte Carlo estimation of expected information gains
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TLDR
An efficient algorithm to estimate the expected information gain by applying a multilevel Monte Carlo (MLMC) method is developed and an antithetic MLMC estimator is introduced to provide a sufficient condition on the data model under which the antithetic property of the MLMC estimation is well exploited such that optimal complexity of is achieved.Abstract:
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 $\theta$ is reduced on average by collecting relevant data $Y$. However, estimating the expected information gain has been considered computationally challenging since it is defined as a nested expectation with an outer expectation with respect to $Y$ and an inner expectation with respect to $\theta$. In fact, the standard, nested Monte Carlo method requires a total computational cost of $O(\varepsilon^{-3})$ to achieve a root-mean-square accuracy of $\varepsilon$. In this paper we develop an efficient algorithm to estimate the expected information gain by applying a multilevel Monte Carlo (MLMC) method. To be precise, we introduce an antithetic MLMC estimator for the expected information gain and provide a sufficient condition on the data model under which the antithetic property of the MLMC estimator is well exploited such that optimal complexity of $O(\varepsilon^{-2})$ is achieved. Furthermore, we discuss how to incorporate importance sampling techniques within the MLMC estimator to avoid arithmetic underflow. Numerical experiments show the considerable computational cost savings compared to the nested Monte Carlo method for a simple test case and a more realistic pharmacokinetic model.read more
Citations
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Multilevel Monte Carlo Estimation of the Expected Value of Sample Information
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Optimal Bayesian experimental design for subsurface flow problems
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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.
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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.
References
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