scholarly journals Bayesian inference of preferential seepage path by gradient-based Markov Chain Monte Carlo

2020 ◽  
Vol 8 (3) ◽  
pp. 59-63
Author(s):  
Kazunori Fujisawa ◽  
Michael Koch ◽  
Akira Murakami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Gradient Based

A gradient-based Markov chain Monte Carlo method for full-waveform inversion and uncertainty analysis

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. R15-R30
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Posterior Distribution ◽  
Waveform Inversion ◽  
Model Space ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Gradient Based

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

Bayesian inference along Markov Chain Monte Carlo approach for PWR core loading pattern optimization

2012 ◽  
Vol 50 ◽  
pp. 150-157 ◽  
Author(s):  
A. Haghighattalab ◽  
A. Minuchehr ◽  
A. Zolfaghari ◽  
F. Khoshahval
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Monte Carlo Approach ◽  
Loading Pattern
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