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September 2016 On Bayesian A- and D-Optimal Experimental Designs in Infinite Dimensions
Alen Alexanderian, Philip J. Gloor, Omar Ghattas
Bayesian Anal. 11(3): 671-695 (September 2016). DOI: 10.1214/15-BA969

Abstract

We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the infinite-dimensional case. To this end, we derive the infinite-dimensional version of the expression for the Kullback–Leibler divergence from the posterior measure to the prior measure, which is subsequently used to derive the expression for the expected information gain. We also study the notion of Bayesian A-optimality in the infinite-dimensional setting, and extend the well known (in the finite-dimensional case) equivalence of the Bayes risk of the MAP estimator with the trace of the posterior covariance, for the Gaussian linear case, to the infinite-dimensional Hilbert space case.

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Alen Alexanderian. Philip J. Gloor. Omar Ghattas. "On Bayesian A- and D-Optimal Experimental Designs in Infinite Dimensions." Bayesian Anal. 11 (3) 671 - 695, September 2016. https://doi.org/10.1214/15-BA969

Information

Published: September 2016
First available in Project Euclid: 26 August 2015

zbMATH: 1359.62315
MathSciNet: MR3498042
Digital Object Identifier: 10.1214/15-BA969

Rights: Copyright © 2016 International Society for Bayesian Analysis

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Vol.11 • No. 3 • September 2016
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