A new Monte Carlo technique: antithetic variates

1956 ◽  
Vol 52 (3) ◽  
pp. 449-475 ◽  
Author(s):  
J. M. Hammersley ◽  
K. W. Morton
Keyword(s):  
Monte Carlo ◽  
Standard Error ◽  
Sampling Technique ◽  
Random Processes ◽  
Main Concern ◽  
Sampling Variance ◽  
Small Standard Error ◽  
Antithetic Variates ◽  
Final Estimate ◽  
Electronic Computers

As we have stressed in a previous paper (9), the main concern in Monte Carlo work is to achieve without inordinate labour a respectably small standard error in the final result. Mere replication of the Monte Carlo results is unrewarding; for, to reduce a standard error by a factor k, the labour must be increased k2-fold, and this will be beyond the resources of even electronic computers when k = 1000, say. The remedy lies in a skilful choice of sampling technique and the substitution of analytical methods for random processes wherever possible. The efficiency of a Monte Carlo process may be taken as inversely proportional to the product of the sampling variance of the final estimate and the amount of labour expended in obtaining this estimate; and it is profitable to allow some increase in the labour if that produces an overwhelming decrease in the variance. For instance, in the last example quoted below (Table 2), we reduce the variance by a factor of four million at the expense of only multiplying the labour sixteenfold, thereby attaining a 250,000-fold gain of efficiency.

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.

Reliability Assessment of Power System Using Importance Sampling Technique Based on Layer Optimization Simulation

2011 ◽  
Vol 88-89 ◽  
pp. 554-558 ◽  
Author(s):  
Bin Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Power System ◽  
Importance Sampling ◽  
System Reliability ◽  
Sampling Method ◽  
Sampling Technique ◽  
Test System ◽  
Importance Sampling Method ◽  
Importance Sampling Technique

An improved importance sampling method with layer simulation optimization is presented in this paper. Through the solution sequence of the components’ optimum biased factors according to their importance degree to system reliability, the presented technique can further accelerate the convergence speed of the Monte-Carlo simulation. The idea is that the multivariate distribution’ optimization of components in power system is transferred to many steps’ optimization based on importance sampling method with different optimum biased factors. The practice is that the components are layered according to their importance degree to the system reliability before the Monte-Carlo simulation, the more forward, the more important, and the optimum biased factors of components in the latest layer is searched while the importance sampling is carried out until the demanded accuracy is reached. The validity of the presented is verified using the IEEE-RTS79 test system.

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 Effect of Super Brain Yoga on Concentration and Memory in Children in a Selected Private School, Kelambakkam, Kanchipuram Dt, Tamilnadu, India

2021 ◽  
pp. 141-149
Author(s):  
V. S. Viji ◽  
S. Subbulakshmi ◽  
L. Uma Devi
Keyword(s):  
Standard Deviation ◽  
Standard Error ◽  
Private School ◽  
Sampling Technique ◽  
Demographic Variables ◽  
School Age ◽  
Long Period ◽  
Self Confidence ◽  
Positive Effect ◽  
Regular Practice

Background: The Sigmund Freud's psychosexual theory says that the school age is the important stage in the development of self-confidence. Many studies reveals that physical exercise has a positive effect in the cognitive intellectual areas of the children. Regular practice of simple exercise will makes the children more sharp minded and helps to give a better learning outcome Material & Methods: The main aim of the study was to evaluate the efficacy of super brain yoga by measuring the changes in concentration and memory in children.. A quantitative evaluative approach was used for this study with a one group pretest and posttest design. The purposive sampling technique was used to select 120 students aged between 10 to 12 years who were studying in 6th and 7th standard. The practice of super brain yoga was given 20 times over 10 minutes per day for a period of one month. The Digit Cancellation Test and the Knox Cube Test was used to was used to assess the pretest and posttest level of concentration and memory in children. Results: The pretest mean and standard deviation of concentration was 33.64±5.43 with a standard error of 0.496. The first posttest (at the end of second week of practice of super brain yoga) mean and standard deviation was 33.55± 5.378 with a standard error of 0.491 and the t-value was 0.749. The second posttest (at the end of fourth week of practice of super brain yoga) mean and standard deviation was 33.67±5.393 with a standard error of 0.492 and the t-value was 0.240. The pretest mean and standard deviation of memory was 33.67±4.696with a standard error of 0.429.The first posttest (at the end of second week of practice of super brain yoga) mean and standard deviation was 33.66±4.654with a standard error of 0.425 and the t-value was 0.080. The second posttest (at the end of fourth week of practice of super brain yoga) mean and standard deviation was 33.68±4.700with a standard error of 0.420and the t-value was 0.074. The present study result shows that statistically there was no significant effect of super brain yoga on concentration and memory of children and no association between posttest level of concentration and memory of children with their selected demographic variables. Conclusion: Hence the study concludes that the super brain yoga has no significant effect on concentration and memory of children with a duration of four weeks of practice.The study recommended that to bring the desired positive effect on children’s concentration and memory the study can be conducted for a long period of time.

scholarly journals The Effect of Participatory Budgets on The Performance of School (Studies in Smk Sumbawa)

2017 ◽  
Vol 1 (2) ◽  
pp. 267
Author(s):  
Siti Nur Aisyah ◽  
Sutrisno Sutrisno ◽  
Erwin Saraswati
Keyword(s):  
Public Schools ◽  
Organizational Commitment ◽  
Leadership Styles ◽  
Sampling Technique ◽  
Simple Random Sampling ◽  
Main Concern ◽  
Participatory Budgeting ◽  
Educational Personnel ◽  
Private And Public ◽  
Vocational High Schools

<p>This study was aimed to empirically analyze the effect of participatory budgeting on the school’s performance with organizational commitment, organizational culture, and leadership styles as the moderating variabels. The populations in this study are educators, educational personnel, committe of 801 people and spread at the vocational high schools in Sumbawa regency comprising 17 private and public schools. The disproportionate stratified simple random sampling was used as sampling technique. There are 278 repondents (educators, educational personnel, committee). The analysis method involved SEM PLS and Smart PLS 2.0 as statistic test tools. The result showed that the participatory budgeting affected the school performances. The organizational commitment and leadership styles were able to moderate the effect of participatory budgeting on performances. The leadership styles focusing on the preference and skill of the subordinates became the main concern and the commitment of the members to the organization supported the performance of the schools.</p><p> </p><p><strong>Keywords:</strong> Participatory Budgeting, Performance, Leadership Styles, Organizaional Culture, Organizational Commitment</p>

scholarly journals ‘Hardcastle Hollows’ in loess landforms: Closed depressions in aeolian landscapes – in a geoheritage context

2018 ◽  
Vol 10 (1) ◽  
pp. 58-63
Author(s):  
Roger Fagg ◽  
Ian Smalley
Keyword(s):  
Monte Carlo ◽  
Random Processes ◽  
Ground Subsidence ◽  
Shape Classification ◽  
Random Shape ◽  
Side Ratio ◽  
Landscape Processes ◽  
Stage Process ◽  
The Mean ◽  
Loess Deposits

Abstract Loess landscapes sometimes contain isolated depressed areas, which often appear as lakes. The outline shape (and distribution) of these depressions could be controlled by random processes, particularly if the depressions are caused by loess hydroconsolidation and ground subsidence. By applying the Zingg system of shape classification it is possible to propose a mean random shape for the closed depressions. A Zingg rectangle with a side ratio of about 2:1 is produced by a very simple Monte Carlo method, which had been used previously to calculate the mean random shape of a loess particle. The Zingg rectangle indicates the basic shape of the mean closed depression. A simple four stage process for the formation of the depressions is proposed. They might be called ‘Hardcastle Hollows’ in honour of John Hardcastle who first reported them, in New Zealand. Studies on Ukrainian deposits suggest that there might be some stratigraphic value in the observation of closed depressions; they are often not superimposed in successive depositions of loess. Hydroconsolidation is important in landscape processes. The hollows provide interesting habitats and enlarge the ecological interest of loess deposits; the geoheritage scene is enhanced.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

2006 ◽  
Vol 17 (11) ◽  
pp. 1527-1549 ◽  
Author(s):  
J. N. CORCORAN ◽  
U. SCHNEIDER ◽  
H.-B. SCHÜTTLER
Keyword(s):  
Monte Carlo ◽  
Feynman Graph ◽  
Sampling Technique ◽  
Small Samples ◽  
Brute Force ◽  
Perfect Sampling ◽  
Self Energy ◽  
Graph Expansions ◽  
Low Dimensional ◽  
True Values

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

Verification of reference ranges by using a Monte Carlo sampling technique

1994 ◽  
Vol 40 (12) ◽  
pp. 2216-2222 ◽  
Author(s):  
E W Holmes ◽  
S E Kahn ◽  
P A Molnar ◽  
E W Bermes
Keyword(s):  
Monte Carlo ◽  
Sampling Technique ◽  
Monte Carlo Sampling ◽  
Monte Carlo Technique ◽  
Reference Ranges ◽  
Operating Characteristics ◽  
Significance Tests ◽  
Software Program

Abstract We have investigated the application of Monte Carlo significance tests to the verification of reference ranges in the context of the transfer of an established range from one laboratory to another. Here we present an introduction to the Monte Carlo technique, outline a procedure for performing these tests using a commercially available software program, and demonstrate some of the operating characteristics of the tests when they are used to compare samples of different sizes and variances.

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