article

Free access

Antithetic variates revisited

Authors:

George S. Fishman,

Baosheng D. HuangAuthors Info & Claims

Communications of the ACM, Volume 26, Issue 11

Pages 964 - 971

https://doi.org/10.1145/182.358462

Published: 01 November 1983 Publication History

PDF eReader

References

[1]

Andreasson, I.J. Combinations of antithetic methods in simulation. Report NA 72.49, Department of Information Processing Computer Science. The Royal Institute of Technology, Stockholm, Sweden, 1972.

Google Scholar

[2]

Andreasson, l.J. and Dahlquist, G. Groups of antithetic transformations in simulation. Report NA 72.57, Department of Information Processing Computer Science, The Royal Institute of Technology, Stockholm, Sweden, 1972.

Google Scholar

[3]

Fishman, G.S. Variance reduction for population growth models. Oper. Res. 27, (1979) 997-1010.

Digital Library

Google Scholar

[4]

Fishman, G.S. Accelerated accuracy in the simulation of Markov chains. Oper. Res. 31 (1983). 466-487.

Google Scholar

[5]

Fishman, G.S. Accelerated convergence in the simulation of countably infinite state Markov chains. TR 81-4. Curriculum in Operations Research and Systems Analysis, University of North Carolina at Chapel Hill, 1981.

Google Scholar

[6]

Fishman, G.S. Superefficient simulation of Markov chains and semi- Markov processes. TR UNC/ORSA/TR-82/5, Curriculum in Operations Research and Systems Analysis, University of North Carolina at Chapel Hill, 1982.

Google Scholar

[7]

Halton, J.H. and Handscomb, D.C. A method for increasing the efficiency of Monte Carlo integration. ACM 4, (1957) 329-340.

Digital Library

Google Scholar

[8]

Hammersley, J.M. and Mauldon, J.G. General principles of antithetic variates. Proc. Cambridge Philosophical Society, 52, (1956) 476-481.

Crossref

Google Scholar

[9]

Hammersley, J.M. and Morton. K.W. A new Monte Carlo technique: Antithetic variates. Proc. Cambridge Philosophical Society, 52, (1956) 449-475.

Crossref

Google Scholar

[10]

Handscomb, D.C. Proof of the antithetic-variates theorems for n > 2. Proc. Cambridge Philosophical Society, 54 (1958), 300-301.

Crossref

Google Scholar

[11]

Huang, B.S. Antithetic sampling method: A variance reduction technique in computer simulation, Unpublished Ph.D. Dissertation, University of North Carolina at Chapel Hill, 1980.

Digital Library

Google Scholar

[12]

Lyness, J.N. and Ninham, B.W. Numerical quadrature and asymptotic expansions. Math. Comput. 21, (1967) 162-178.

Crossref

Google Scholar

[13]

Mardia. K.V. Families of Bivariate Distributions, London: Griffin Statistical Monographs, 1970.

Google Scholar

[14]

Roach, W.L. Antithetic sampling in system simulation. Unpublished Ph.D. Thesis, School of Business Administration, The University of Michigan, 1973.

Google Scholar

[15]

Whitt, W. Bivariate distributions with given marginals. Ann. Statistics, 4 (1976), 1280-1289.

Crossref

Google Scholar

[16]

Wilson, J.R. Proof of the antithetic-variates theorem for unbounded functions. Math. Proc. of the Cambridge Philosophical Society, 86 (1979), 477-479.

Crossref

Google Scholar

Cited By

View all

Casarin RCraiu RFrattarolo LRobert C(2024)Living on the Edge: An Unified Approach to Antithetic SamplingStatistical Science10.1214/23-STS88839:1Online publication date: 1-Feb-2024
https://doi.org/10.1214/23-STS888
(2023)ReferencesHamiltonian Monte Carlo Methods in Machine Learning10.1016/B978-0-44-319035-3.00033-1(175-184)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-319035-3.00033-1
Marwala TMongwe WMbuvha R(2023)Introduction to Hamiltonian Monte CarloHamiltonian Monte Carlo Methods in Machine Learning10.1016/B978-0-44-319035-3.00013-6(1-29)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-319035-3.00013-6
Show More Cited By

Index Terms

Antithetic variates revisited
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods

Recommendations

Combining antithetic variates and control variates in simulation experiments

Antithetic variates and control variates are two well-known variance reduction techniques. We consider combining antithetic variates and control variates to estimate the mean response in a stochastic simulation experiment. When applying antithetic ...
Variance reduction in sample approximations of stochastic programs

This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to Monte Carlo (...
Using sectioning to construct confidence intervals for quantiles when applying antithetic variates
SummerSim '14: Proceedings of the 2014 Summer Simulation Multiconference

We use sectioning to construct a confidence interval (CI) for a quantile when applying antithetic variates, which is a well-known variance-reduction technique. Closely related to batching, sectioning starts with the batching CI and replaces the batching ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Communications of the ACM Volume 26, Issue 11

Nov. 1983

203 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/182

Editor:
Peter J. Denning
NASA Ames Research Center, Moffett Field, CA

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 1983

Published in CACM Volume 26, Issue 11

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

35
Total Citations
View Citations
1,022
Total Downloads

Downloads (Last 12 months)155
Downloads (Last 6 weeks)50

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Casarin RCraiu RFrattarolo LRobert C(2024)Living on the Edge: An Unified Approach to Antithetic SamplingStatistical Science10.1214/23-STS88839:1Online publication date: 1-Feb-2024
https://doi.org/10.1214/23-STS888
(2023)ReferencesHamiltonian Monte Carlo Methods in Machine Learning10.1016/B978-0-44-319035-3.00033-1(175-184)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-319035-3.00033-1
Marwala TMongwe WMbuvha R(2023)Introduction to Hamiltonian Monte CarloHamiltonian Monte Carlo Methods in Machine Learning10.1016/B978-0-44-319035-3.00013-6(1-29)Online publication date: 2023
https://doi.org/10.1016/B978-0-44-319035-3.00013-6
Mongwe WMbuvha RMarwala T(2021)Antithetic Magnetic and Shadow Hamiltonian Monte CarloIEEE Access10.1109/ACCESS.2021.30691969(49857-49867)Online publication date: 2021
https://doi.org/10.1109/ACCESS.2021.3069196
Park JChoe G(2016)A new variance reduction method for option pricing based on sampling the vertices of a simplexQuantitative Finance10.1080/14697688.2015.111671016:8(1165-1173)Online publication date: 20-Apr-2016
https://doi.org/10.1080/14697688.2015.1116710
Caro JMöller JKarnon JStahl JIshak J(2015)ReferencesDiscrete Event Simulation for Health Technology Assessment10.1201/b19421-12(325-342)Online publication date: 15-Oct-2015
https://doi.org/10.1201/b19421-12
Adewunmi AAickelin U(2012)Investigating the Effectiveness of Variance Reduction Techniques in Manufacturing, Call Center and Cross-Docking Discrete Event Simulation ModelsUse Cases of Discrete Event Simulation10.1007/978-3-642-28777-0_1(1-26)Online publication date: 2012
https://doi.org/10.1007/978-3-642-28777-0_1
Akroyd JSmith AMcGlashan LKraft M(2010)Comparison of the stochastic fields method and DQMoM-IEM as turbulent reaction closuresChemical Engineering Science10.1016/j.ces.2010.06.03965:20(5429-5441)Online publication date: Oct-2010
https://doi.org/10.1016/j.ces.2010.06.039
Alexopoulos CGoldsman DWilson J(2009)George Fishman’s Professional CareerAdvancing the Frontiers of Simulation10.1007/b110059_1(1-19)Online publication date: 17-Jul-2009
https://doi.org/10.1007/b110059_1
Ben-Ameur HL'Ecuyer PLemieux C(2004)Combination of General Antithetic Transformations and Control VariablesMathematics of Operations Research10.1287/moor.1040.010129:4(946-960)Online publication date: 1-Nov-2004
https://dl.acm.org/doi/10.1287/moor.1040.0101
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

Combining antithetic variates and control variates in simulation experiments

Variance reduction in sample approximations of stochastic programs

Using sectioning to construct confidence intervals for quantiles when applying antithetic variates

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations