A transport-based multifidelity preconditioner for Markov chain Monte Carlo
Author(s)Peherstorfer, Benjamin; Marzouk, Youssef M
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Markov chain Monte Carlo (MCMC) sampling of posterior distributions arising in Bayesian inverse problems is challenging when evaluations of the forward model are computationally expensive. Replacing the forward model with a low-cost, low-fidelity model often significantly reduces computational cost; however, employing a low-fidelity model alone means that the stationary distribution of the MCMC chain is the posterior distribution corresponding to the low-fidelity model, rather than the original posterior distribution corresponding to the high-fidelity model. We propose a multifidelity approach that combines, rather than replaces, the high-fidelity model with a low-fidelity model. First, the low-fidelity model is used to construct a transport map that deterministically couples a reference Gaussian distribution with an approximation of the low-fidelity posterior. Then, the high-fidelity posterior distribution is explored using a non-Gaussian proposal distribution derived from the transport map. This multifidelity “preconditioned” MCMC approach seeks efficient sampling via a proposal that is explicitly tailored to the posterior at hand and that is constructed efficiently with the low-fidelity model. By relying on the low-fidelity model only to construct the proposal distribution, our approach guarantees that the stationary distribution of the MCMC chain is the high-fidelity posterior. In our numerical examples, our multifidelity approach achieves significant speedups compared with single-fidelity MCMC sampling methods.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
Advances in computational mathematics
Springer Science and Business Media LLC
Peherstorfer, Benjamin and Youssef Marzouk. “A transport-based multifidelity preconditioner for Markov chain Monte Carlo.” Advances in computational mathematics, vol. 45 2019, pp. 2321-2348 © 2019 The Author(s)