Handle URI:
http://hdl.handle.net/10754/624067
Title:
Bayesian Optimal Experimental Design Using Multilevel Monte Carlo
Authors:
Ben Issaid, Chaouki ( 0000-0002-4481-8168 ) ; Long, Quan ( 0000-0002-0329-9437 ) ; Scavino, Marco ( 0000-0001-5114-853X ) ; Tempone, Raul ( 0000-0003-1967-4446 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorBen Issaid, Chaoukien
dc.contributor.authorLong, Quanen
dc.contributor.authorScavino, Marcoen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-05T08:35:47Z-
dc.date.available2017-06-05T08:35:47Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624067-
dc.description.abstractExperimental 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.en
dc.titleBayesian Optimal Experimental Design Using Multilevel Monte Carloen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
kaust.authorBen Issaid, Chaoukien
kaust.authorLong, Quanen
kaust.authorScavino, Marcoen
kaust.authorTempone, Raulen
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