Bayesian seismic inversion: Measuring Langevin MCMC sample quality with kernels
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segam2020-3422419.1.pdf
Description
Published version
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682.89 KB
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Checksum (MD5)
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Author(s)
Izzatullah, Muhammad
Baptista, Ricardo
Mackey, Lester
Marzouk, Youssef
Peter, Daniel
Date Issued
September 25, 2020
Journal
SEG Technical Program Expanded Abstracts 2020
Publisher
Society of Exploration Geophysicists
Citation
Muhammad Izzatullah, Ricardo Baptista, Lester Mackey, Youssef Marzouk, Daniel Peter; September 1, 2020. "Bayesian seismic inversion: Measuring Langevin MCMC sample quality with kernels." Proceedings of the SEG Technical Program Expanded Abstracts 2020. SEG Technical Program Expanded Abstracts 2020. (pp. pp. 295-299). ASME.
Version
Final published version
Abstract
The Bayesian framework is commonly used to quantify uncertainty in seismic inversion. To perform Bayesian inference, Markov chain Monte Carlo (MCMC) algorithms are regarded as the gold standard technique for sampling from the posterior probability distribution. Consistent MCMC methods have trouble for complex, high-dimensional models, and most methods scale poorly to large datasets, such as those arising in seismic inversion. As an alternative, approximate MCMC methods based on unadjusted Langevin dynamics offer scalability and more rapid sampling at the cost of biased inference. However, when assessing the quality of approximate MCMC samples for characterizing the posterior distribution, most diagnostics fail to account for these biases. In this work, we introduce the kernel Stein discrepancy (KSD) as a diagnostic tool to determine the convergence of MCMC samples for Bayesian seismic inversion. We demonstrate the use of the KSD for measuring sample quality and selecting the optimal Langevin MCMC algorithm for two Gaussian Bayesian inference problems.
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1190/segam2020-3422419.1
