Markov Chain Monte Carlo Uncertainty Quantification with a Least-Squares Support Vector Regression Proxy

2019 ◽  
Author(s):  
Emilio Paulo dos Santos Sousa ◽  
Albert C. Reynolds
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Least Squares ◽  
Uncertainty Quantification ◽  
Support Vector Regression ◽  
Support Vector

A two-stage Markov chain Monte Carlo method for seismic inversion and uncertainty quantification

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R1003-R1020 ◽  
Author(s):  
Georgia K. Stuart ◽  
Susan E. Minkoff ◽  
Felipe Pereira
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Quantification ◽  
Bayesian Methods ◽  
Posterior Distributions ◽  
Mcmc Algorithm ◽  
Two Stage ◽  
Fine Grid ◽  
Highest Posterior Density

Bayesian methods for full-waveform inversion allow quantification of uncertainty in the solution, including determination of interval estimates and posterior distributions of the model unknowns. Markov chain Monte Carlo (MCMC) methods produce posterior distributions subject to fewer assumptions, such as normality, than deterministic Bayesian methods. However, MCMC is computationally a very expensive process that requires repeated solution of the wave equation for different velocity samples. Ultimately, a large proportion of these samples (often 40%–90%) is rejected. We have evaluated a two-stage MCMC algorithm that uses a coarse-grid filter to quickly reject unacceptable velocity proposals, thereby reducing the computational expense of solving the velocity inversion problem and quantifying uncertainty. Our filter stage uses operator upscaling, which provides near-perfect speedup in parallel with essentially no communication between processes and produces data that are highly correlated with those obtained from the full fine-grid solution. Four numerical experiments demonstrate the efficiency and accuracy of the method. The two-stage MCMC algorithm produce the same results (i.e., posterior distributions and uncertainty information, such as medians and highest posterior density intervals) as the Metropolis-Hastings MCMC. Thus, no information needed for uncertainty quantification is compromised when replacing the one-stage MCMC with the more computationally efficient two-stage MCMC. In four representative experiments, the two-stage method reduces the time spent on rejected models by one-third to one-half, which is important because most of models tried during the course of the MCMC algorithm are rejected. Furthermore, the two-stage MCMC algorithm substantially reduced the overall time-per-trial by as much as 40%, while increasing the acceptance rate from 9% to 90%.

scholarly journals High performance uncertainty quantification with parallelized multilevel Markov chain Monte Carlo

2021 ◽  
Author(s):  
Linus Seelinger ◽  
Anne Reinarz ◽  
Leonhard Rannabauer ◽  
Michael Bader ◽  
Peter Bastian ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Quantification ◽  
High Performance ◽  
Performance Uncertainty
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