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A perspective on variance reduction in dynamic simulation experiments. (English) Zbl 0627.65149

We herein have a unifying survey on variance reduction strategies. The basis of this survey is a taxonomy that considers variance reduction techniques as the composition of six elementary classes; and this taxonomy is first reviewed in full detail. In addition, the variance reduction problem is defined as a constraint optimization problem.
The six basic classes in question are distribution replacement, dependence induction, equivalent allocation, sample allocation, equivalent information and auxiliary information. There implications with respect to variance reduction are carefully examined, and some examples are outlined.
Reviewer: G.Jumarie

MSC:

65C99 Probabilistic methods, stochastic differential equations
62K05 Optimal statistical designs
62J10 Analysis of variance and covariance (ANOVA)
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References:

[1] Bickel PJ, Mathematical Statistics, Basic Ideas and Selected Topics (1977)
[2] Bratley P, A Guide to Simulation (1983)
[3] DOI: 10.1287/mnsc.18.3.207 · Zbl 0227.90020
[4] Carson J.S, 1977 Winter Simulation Conference Proceedings pp 187– (1977)
[5] DOI: 10.1287/opre.28.3.535 · Zbl 0438.60084
[6] DOI: 10.1287/mnsc.21.6.607 · Zbl 0355.62016
[7] DOI: 10.2172/4167844
[8] DOI: 10.1080/00949658508810795 · Zbl 0611.62069
[9] Cochran W.G, Sampling Techniques (1977)
[10] DOI: 10.1111/j.1540-5915.1982.tb00150.x
[11] DOI: 10.1111/j.1540-5915.1983.tb00174.x
[12] Dalenius T, Skandinavisk Aktuarietidskrift 33 pp 203– (1950)
[13] Dalenius T, Skandinavisk Aktuarietidskrift 34 pp 133– (1951)
[14] DOI: 10.1287/mnsc.31.5.579 · Zbl 0607.62125
[15] DOI: 10.1002/nav.3800320206 · Zbl 0576.90051
[16] DOI: 10.1145/182.358462 · Zbl 0535.65100
[17] DOI: 10.2307/2683661
[18] DOI: 10.1016/0167-6377(86)90076-3 · Zbl 0612.60081
[19] Glynn P.W, 1983 Winter Simulation Conference Proceedings pp 39– (1983)
[20] Granovsky B.L, Mathematische, Physikalische und Technische Wissenschaften 192 pp 329– (1983)
[21] DOI: 10.1287/opre.30.3.515 · Zbl 0491.60096
[22] Hammersley J.M, Monte Carlo Methods (1964)
[23] DOI: 10.1017/S0305004100031467
[24] DOI: 10.1017/S0305004100033454
[25] DOI: 10.1016/0378-4754(79)90136-8 · Zbl 0407.90030
[26] DOI: 10.1109/TCOM.1984.1095970
[27] Kahn H, inSymposium on Monte Carlo Methods pp 146– (1956)
[28] Kendall M, The Advanced Theory of Statistics Inference and Relationships 2 (1979) · Zbl 0416.62001
[29] Kioussis L.C, Winter Simulation Conference Proceedings 2 pp 631– (1983)
[30] Kleijnen J.P.C, Statistical Techniques in Simulation (1974) · Zbl 0316.65002
[31] Kleijnen, J.P.C. 1985, ”Analyzing Simulation Experiments with Common Random Numbers” Research Memorandum, Department of Economics, Tilburg University, The Netherlands.
[32] DOI: 10.1287/opre.30.1.182 · Zbl 0481.90024
[33] Lavenberg, S.S and Welch, P.D. 1979. ”Using Conditional Expectation to Reduce Variance in Discrete Event Simulation”. Edited by: Highland, H and Spiegel, M. 291–294. Winter Simulation Conference Proceedings.
[34] DOI: 10.1287/mnsc.27.3.322 · Zbl 0452.65004
[35] DOI: 10.1287/mnsc.22.1.30 · Zbl 0328.60055
[36] Law A.M, Simulation Modeling and Analysis (1982) · Zbl 0489.65007
[37] DOI: 10.1214/aoms/1177731312 · Zbl 0063.03701
[38] Marshall, A.W. 1956. ”The Use of Multi-Stage Sampling Schemes in Monte Carlo Computations”. Edited by: Meyer, H. NY: Symposium of Monte Carlo Methods.
[39] McGrath, E.J. and D.C. Irving \(year:1973"Techniques for Efficient Monte Carlo Simulation, Vol. Ill, Variance Reduction" ORNL Report SAI-72-509-LJ.\)
[40] DOI: 10.2307/1268522 · Zbl 0415.62011
[41] DOI: 10.1080/00949657408810067 · Zbl 0291.62098
[42] DOI: 10.1287/opre.31.5.966 · Zbl 0535.60094
[43] Nelson, B.L. 1985.A Decomposition Approach to Variance Reduction, Edited by: Blais, G, Gantz, D and Solomon, S. 23–32. Winter Simulation Conference Proceedings.
[44] Nelson B.L, Trans, Society for Computer Simulation 2 pp 237– (1985)
[45] Nelson B.L, Computers & Operations Research (1987)
[46] Nelson, B.L and Schmeiser, B. 1983.Variance Reduction:Basic Transformations, Edited by: Roberts, S, Banks, J and Schmeiser, B. 255–258. Winter Simulation Conference Proceedings.
[47] Nelson B.L, Department of Industrial and Systems Engineering (1986)
[48] DOI: 10.1080/00949658608810871
[49] DOI: 10.1080/07408178408974681
[50] Nozari, A., S.F,Arnold and CD,Pegden 1984”Statistical Analysis Under Schruben and Margolin Correlation Induction Strategy Technical Report, School of Industrial Engineering, Univ. of Oklahoma.
[51] Porta Nova, A.M.O and Wilson, J.R. 1986.Using Control Variates to Estimate Multiresponse Simulation Metamodels, Edited by: Wilson, J, Henrikson, S and Roberts, S. 326–334. Winter Simulation Conference Proceedings.
[52] DOI: 10.1002/9780470316436 · Zbl 0256.62002
[53] DOI: 10.1080/00949657708810144 · Zbl 0347.62011
[54] DOI: 10.1287/mnsc.31.2.224 · Zbl 0606.62094
[55] DOI: 10.1002/9780470316511
[56] DOI: 10.1287/opre.33.3.661 · Zbl 0606.65100
[57] DOI: 10.1287/mnsc.31.1.66 · Zbl 0606.65099
[58] DOI: 10.1111/j.1540-5915.1982.tb00151.x
[59] DOI: 10.1111/j.1540-5915.1983.tb00175.x
[60] Schmeiser, B and Kachitvichyanukul, V. 1986.Correlation Induction Without the Inverse Transform, Edited by: Wilson, J, Henrikson, J and Roberts, S. 266–274. Winter Simulation Conference Proceedings.
[61] Schruben L.W, Current Issues in Computer Simulation (1979)
[62] DOI: 10.2307/2286590 · Zbl 0386.62010
[63] DOI: 10.1111/j.1467-842X.1963.tb00134.x · Zbl 0113.13705
[64] DOI: 10.1016/0378-4754(79)90007-7 · Zbl 0416.90030
[65] DOI: 10.2307/2347234
[66] DOI: 10.1111/j.1467-9574.1984.tb01099.x
[67] Stein, M. 1985 ”The Use of Latin Hypercube Sampling for Variance Reduction in Simulations with Many Random Parameters” Research Report RC 11166 (#50265), IBM T.J. Watson Research Center, Yorktown Heights, NY.
[68] Tew, J.D and Wilson, J.R. 1985.Validation of Correlation Induction Strategies for Simulation Experiments, Edited by: Blais, G, Gantz, D and Solomon, S. 190–195. Winter Simulation Conference Proceedings.
[69] Venkatraman, S.1983 ”Application of the Control Variate Technique to Multiple Simulation Output Analysis” unpublished M.S. thesis, Department of Mechanical Engineering, University of Texas, Austin, Texas.
[70] DOI: 10.1016/0167-6377(86)90098-2
[71] DOI: 10.1214/aos/1176343660 · Zbl 0367.62022
[72] DOI: 10.1287/moor.5.4.494 · Zbl 0447.60074
[73] DOI: 10.1017/S0305004100056334 · Zbl 0415.62020
[74] Wilson J.R, Am. J, Math. Mgmt ScL 3 pp 121– (1983)
[75] Wilson J.R, Am, J. Math, Mgmt. ScL 3 pp 277– (1984)
[76] DOI: 10.1080/00949658408810723 · Zbl 0569.65100
[77] DOI: 10.1287/mnsc.30.12.1459 · Zbl 0549.60094
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