scholarly journals Schedules of lectures and Monte Carlo method

2011 ◽  
Vol 52 ◽  
Author(s):  
Nikolaj Grigorjev ◽  
Gediminas Stepanauskas
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Simulated Annealing ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Simulated Annealing Algorithm ◽  
Annealing Algorithm

In this paper the problem of the construction of schedule of lectures is considered. The Markov chain Monte Carlo method is used. A particular program based on simulated annealing algorithm was created.  

On the Markov Chain Simulation Method for Uniform Combinatorial Distributions and Simulated Annealing

1987 ◽  
Vol 1 (1) ◽  
pp. 33-46 ◽  
Author(s):  
David Aldous
Keyword(s):  
Markov Chain ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Simulation Method ◽  
Careful Analysis ◽  
Eigenvalue Estimate ◽  
Uniform Distributions ◽  
Markov Chain Method ◽  
Annealing Algorithm ◽  
Second Largest Eigenvalue

Uniform distributions on complicated combinatorial sets can be simulated by the Markov chain method. A condition is given for the simulations to be accurate in polynomial time. Similar analysis of the simulated annealing algorithm remains an open problem. The argument relies on a recent eigenvalue estimate of Alon [4]; the only new mathematical ingredient is a careful analysis of how the accuracy of sample averages of a Markov chain is related to the second-largest eigenvalue.

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.

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