High-depth-resolution Rutherford backscattering data and error analysis of SiGe systems using the simulated annealing and Markov chain Monte Carlo algorithms

1999 ◽  
Vol 59 (7) ◽  
pp. 5097-5105 ◽  
Author(s):  
N. P. Barradas ◽  
A. P. Knights ◽  
C. Jeynes ◽  
O. A. Mironov ◽  
T. J. Grasby ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Simulated Annealing ◽  
Markov Chain Monte Carlo ◽  
Error Analysis ◽  
Depth Resolution ◽  
Rutherford Backscattering ◽  
Monte Carlo Algorithms ◽  
High Depth

Velocity log upscaling based on reversible jump Markov chain Monte Carlo simulated annealing

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R293-R305 ◽  
Author(s):  
Sireesh Dadi ◽  
Richard Gibson ◽  
Kainan Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Simulated Annealing ◽  
Markov Chain Monte Carlo ◽  
Random Perturbation ◽  
Current Model ◽  
Sampling Technique ◽  
Maximum Deviation ◽  
Reversible Jump ◽  
Layer Boundary

Upscaling log measurements acquired at high frequencies and correlating them with corresponding low-frequency values from surface seismic and vertical seismic profile data is a challenging task. We have applied a sampling technique called the reversible jump Markov chain Monte Carlo (RJMCMC) method to this problem. A key property of our approach is that it treats the number of unknowns itself as a parameter to be determined. Specifically, we have considered upscaling as an inverse problem in which we considered the number of coarse layers, layer boundary depths, and material properties as the unknowns. The method applies Bayesian inversion, with RJMCMC sampling and uses simulated annealing to guide the optimization. At each iteration, the algorithm will randomly move a boundary in the current model, add a new boundary, or delete an existing boundary. In each case, a random perturbation is applied to Backus-average values. We have developed examples showing that the mismatch between seismograms computed from the upscaled model and log velocities improves by 89% compared to the case in which the algorithm is allowed to move boundaries only. The layer boundary distributions after running the RJMCMC algorithm can represent sharp and gradual changes in lithology. The maximum deviation of upscaled velocities from Backus-average values is less than 10% with most of the values close to zero.

scholarly journals Convergence of adaptive and interacting Markov chain Monte Carlo algorithms

2011 ◽  
Vol 39 (6) ◽  
pp. 3262-3289 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
P. Priouret
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Algorithms

scholarly journals In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p

Biometrika ◽  
2020 ◽  
Author(s):  
J E Griffin ◽  
K G Łatuszyński ◽  
M F J Steel
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Variable Selection ◽  
Adaptive Design ◽  
Mixing Time ◽  
Bayesian Variable Selection ◽  
Monte Carlo Algorithms ◽  
Large Numbers ◽  
Large P Small N

Summary The availability of datasets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these datasets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. We propose new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large-$p$, small-$n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable nonlocal proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speed-ups of up to four orders of magnitude are observed.

Sign in / Sign up

Export Citation Format

Share Document