Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions
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.
Keywords
Cite
@article{arxiv.1603.02004,
title = {Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions},
author = {Andrew M. Stuart and Aretha L. Teckentrup},
journal= {arXiv preprint arXiv:1603.02004},
year = {2024}
}
Comments
In the latest version, we have added Assumption A. This is required in the proofs of Corollaries 4.3, 4.10 and 4.12, and we would like to thank Holger Wendland for alerting us of this omission. The latest version further corrects the definition of X at the beginning of section 2