scholarly journals The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions

2018 ◽  
Vol 19 (2) ◽  
pp. 339-356 ◽  
Author(s):  
L. A. Grzelak ◽  
J. A. S. Witteveen ◽  
M. Suárez-Taboada ◽  
C. W. Oosterlee
Keyword(s):  
Monte Carlo ◽  
Stochastic Collocation ◽  
Highly Efficient ◽  
Efficient Sampling

scholarly journals Optimal sampling in a noisy genetic algorithm for risk-based remediation design

2003 ◽  
Vol 5 (1) ◽  
pp. 11-25 ◽  
Author(s):  
Gayathri Gopalakrishnan ◽  
Barbara S. Minsker ◽  
David E. Goldberg
Keyword(s):  
Genetic Algorithm ◽  
Monte Carlo Simulation ◽  
Genetic Algorithms ◽  
Monte Carlo ◽  
Fitness Function ◽  
Sampling Strategies ◽  
Robust Designs ◽  
Highly Efficient ◽  
Efficient Sampling

A groundwater management model has been developed that predicts human health risks and uses a noisy genetic algorithm to identify promising risk-based corrective action (RBCA) designs. Noisy genetic algorithms are simple genetic algorithms that operate in noisy environments. The noisy genetic algorithm uses a type of noisy fitness function (objective function) called the sampling fitness function, which utilises Monte-Carlo-type sampling to find robust designs. Unlike Monte Carlo simulation modelling, however, the noisy genetic algorithm is highly efficient and can identify robust designs with only a few samples per design. For hydroinformatic problems with complex fitness functions, however, it is important that the sampling be as efficient as possible. In this paper, methods for identifying efficient sampling strategies are investigated and their performance evaluated using a case study of a RBCA design problem. Guidelines for setting the parameter values used in these methods are also developed. Applying these guidelines to the case study resulted in highly efficient sampling strategies that found RBCA designs with 98% reliability using as few as 4 samples per design. Moreover, these designs were identified with fewer simulation runs than would likely be required to identify designs using trial-and-error Monte Carlo simulation. These findings show considerable promise for applying these methods to complex hydroinformatic problems where substantial uncertainty exists but extensive sampling cannot feasibly be done.

scholarly journals Identification of Efficient Sampling Techniques for Probabilistic Voltage Stability Analysis of Renewable-Rich Power Systems

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2328
Author(s):  
Mohammed Alzubaidi ◽  
Kazi N. Hasan ◽  
Lasantha Meegahapola ◽  
Mir Toufikur Rahman
Keyword(s):  
Monte Carlo ◽  
Stability Analysis ◽  
Power Systems ◽  
Large Scale ◽  
Voltage Stability ◽  
Sampling Technique ◽  
Coefficient Of Determination ◽  
Sampling Techniques ◽  
Quasi Monte Carlo ◽  
Efficient Sampling

This paper presents a comparative analysis of six sampling techniques to identify an efficient and accurate sampling technique to be applied to probabilistic voltage stability assessment in large-scale power systems. In this study, six different sampling techniques are investigated and compared to each other in terms of their accuracy and efficiency, including Monte Carlo (MC), three versions of Quasi-Monte Carlo (QMC), i.e., Sobol, Halton, and Latin Hypercube, Markov Chain MC (MCMC), and importance sampling (IS) technique, to evaluate their suitability for application with probabilistic voltage stability analysis in large-scale uncertain power systems. The coefficient of determination (R2) and root mean square error (RMSE) are calculated to measure the accuracy and the efficiency of the sampling techniques compared to each other. All the six sampling techniques provide more than 99% accuracy by producing a large number of wind speed random samples (8760 samples). In terms of efficiency, on the other hand, the three versions of QMC are the most efficient sampling techniques, providing more than 96% accuracy with only a small number of generated samples (150 samples) compared to other techniques.

Monte Carlo method for highly efficient and accurate statistical lithography simulations

2002 ◽  
Author(s):  
Sergei V. Postnikov ◽  
Kevin Lucas ◽  
Karl Wimmer ◽  
Vladimir Ivin ◽  
Andrey Rogov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Highly Efficient

Efficient History Matching Using the Markov-Chain Monte Carlo Method by Means of the Transformed Adaptive Stochastic Collocation Method

SPE Journal ◽  
2019 ◽  
Vol 24 (04) ◽  
pp. 1468-1489 ◽  
Author(s):  
Qinzhuo Liao ◽  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Collocation Method ◽  
Posterior Distribution ◽  
History Matching ◽  
Stochastic Collocation ◽  
Mcmc Method ◽  
Stochastic Collocation Method ◽  
Surrogate System

Summary Bayesian inference provides a convenient framework for history matching and prediction. In this framework, prior knowledge, system nonlinearity, and measurement errors can be directly incorporated into the posterior distribution of the parameters. The Markov-chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior distribution. However, the MCMC method usually requires a large number of forward simulations. Hence, it can be a computationally intensive task, particularly when dealing with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model outputs in the form of polynomials using the stochastic collocation method (SCM). In addition, we use interpolation with the nested sparse grids and adaptively take into account the different importance of parameters for high-dimensional problems. Furthermore, we introduce an additional transform process to improve the accuracy of the surrogate model in case of strong nonlinearities, such as a discontinuous or unsmooth relation between the input parameters and the output responses. Once the surrogate system is built, we can evaluate the likelihood with little computational cost. Numerical results demonstrate that the proposed method can efficiently estimate the posterior statistics of input parameters and provide accurate results for history matching and prediction of the observed data with a moderate number of parameters.

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