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Multilevel Monte Carlo estimation of expected information gains

Content Provider	Scilit
Author	Goda, Takashi Hironaka, Tomohiko Iwamoto, Takeru
Copyright Year	2019
Description	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 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 θ. In fact, the standard, nested Monte Carlo method requires a total computational cost of $O(ε-3) to achieve a root-mean-square accuracy of ε. In this paper we develop an efficient algorithm to estimate the expected information gain by applying a multilevel Monte Carlo (MLMC) method. To be precise, we introduce an antithetic MLMC estimator for the expected information gain and provide a sufficient condition on the data model under which the antithetic property of the MLMC estimator is well exploited such that optimal complexity ofO(ε-2) is achieved. Furthermore, we discuss how to incorporate importance sampling techniques within the MLMC estimator to avoid arithmetic underflow. Numerical experiments show the considerable computational cost savings compared to the nested Monte Carlo method for a simple test case and a more realistic pharmacokinetic model.$
Related Links	http://arxiv.org/pdf/1811.07546
Ending Page	600
Page Count	20
Starting Page	581
ISSN	07362994
e-ISSN	15329356
DOI	10.1080/07362994.2019.1705168
Journal	Stochastic Analysis and Applications
Issue Number	4
Volume Number	38
Language	English
Publisher	Informa UK Limited
Publisher Date	2019-12-26
Access Restriction	Open
Subject Keyword	Journal: Stochastic Analysis and Applications Statistics and Probability Expected Information Gain Bayesian Experimental Design Multilevel Monte Carlo 65c05 94a17
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Statistics, Probability and Uncertainty

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