Bayesian seismic inversion: Measuring Langevin MCMC sample quality with kernels

Muhammad Izzatullah, Ricardo Baptista, Lester Mackey, Youssef Marzouk, Daniel Peter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish (US)
Title of host publicationSEG Technical Program Expanded Abstracts 2020
PublisherSociety of Exploration Geophysicists
DOIs
StatePublished - Sep 25 2020

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