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Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions

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Original languageEnglish
Pages (from-to)721-753
Number of pages33
JournalMathematics of computation
Volume87
Early online date3 Aug 2017
DOIs
Publication statusPublished - 2018

Abstract

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior distribution and various approximations based on the Gaussian process emulator. Our analysis includes approximations based on the mean of the predictive process, as well as approximations based on the full Gaussian process emulator. Our results show that the Hellinger distance between the true posterior and its approximations can be bounded by moments of the error in the emulator. Numerical results confirm our theoretical findings.

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