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Why the Monte Carlo method is so important today

Opinion

Dirk P. Kroese, Tim Brereton, Thomas Taimre, Zdravko I. Botev

Published Online: Jun 20 2014

DOI: 10.1002/wics.1314

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Since the beginning of electronic computing, people have been interested in carrying out random experiments on a computer. Such Monte Carlo techniques are now an essential ingredient in many quantitative investigations. Why is the Monte Carlo method (MCM) so important today? This article explores the reasons why the MCM has evolved from a ‘last resort’ solution to a leading methodology that permeates much of contemporary science, finance, and engineering. WIREs Comput Stat 2014, 6:386–392. doi: 10.1002/wics.1314 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical Models > Simulation Models

References

Kroese, DP, Chan, JCC. Statistical Modeling and Computation. New York: Springer-Verlag; 2014.
Elperin, T, Gertsbakh, IB, Lomonosov, M. Estimation of network reliability using graph evolution models. IEEE Trans Reliab 1991, 40:572–581.
Fishman, GS. Monte Carlo: Concepts, Algorithms and Applications. New York: Springer‐Verlag; 1996.
Law, AM, Kelton, WD. Simulation Modeling and Analysis. 3rd ed. New York: McGraw‐Hill; 2000.
Rubinstein, RY, Kroese, DP. Simulation and the Monte Carlo Method. 2nd ed. New York: John Wiley %26 Sons; 2007.
Kroese, DP, Taimre, T, Botev, ZI. Handbook of Monte Carlo Methods. New York: John Wiley %26 Sons; 2011.
Rubinstein, RY, Kroese, DP. The Cross‐Entropy Method: A Unified Approach to Combinatorial Optimization, Monte‐Carlo Simulation, and Machine Learning. New York: Springer‐Verlag; 2004.
Choset, H, Lynch, KM, Hutchinson, S, Kantor, GA, Burgard, W, Kavraki, LE, Thrun, S. Principles of Robot Motion: Theory, Algorithms, and Implementations. Cambridge, MA: MIT Press; 2005.
Kavraki, LE, Svestka, P, Latombe, J‐C, Overmars, MH. Probabilistic roadmaps for path planning in high‐dimensional configuration spaces. IEEE Trans Robot Autom 1996, 12:566–580.
Metropolis, N. The beginning of the Monte Carlo method. Los Alamos Sci 1987, 15:125–130.
Metropolis, N, Rosenbluth, AW, Rosenbluth, MN, Teller, AH, Teller, E. Equations of state calculations by fast computing machines. J Chem Phys 1953, 21:1087–1092.
Ljungberg, M, Strand, S‐E, King, MA, eds. Monte Carlo Calculations in Nuclear Medicine, Second Edition: Applications in Diagnostic Imaging. Boca Raton, FL: CRC Press; 2012.
Sauvan, P, Sanz, J, Ogando, F. New capabilities for Monte Carlo simulation of deuteron transport and secondary products generation. Nucl Instrum Methods Phys Res A 2010, 614:323–330.
Gillespie, DT. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 1976, 22:403–434.
Gillespie, DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977, 81:2340–2361.
Tuchin, VV. Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis. 2nd ed. Bellingham, WA: SPIE Press; 2007.
Springel, V. The cosmological simulation code gadget‐2. Mon Not R Astron Soc 2005, 364:1105–1134.
Badano, A, Kanicki, J. Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light‐emitting devices. J Appl Phys 2001, 90:1827–1830.
Mesta, M, Carvelli, M, de Vries, RJ, van Eersel, H, van der Holst, JJM, Schober, M, Furno, M, Lüssem, B, Leo, K, Loebl, P, et al. Molecular‐scale simulation of electroluminescence in a multilayer white organic light‐emitting diode. Nat Mater 2013, 12:652–658.
Stenzel, O, Koster, LJA, Thiedmann, R, Oosterhout, SD, Janssen, RAJ, Schmidt, V. A new approach to model‐based simulation of disordered polymer blend solar cells. Adv Funct Mater 2012, 22:1236–1244.
Thiedmann, R, Stenzel, O, Spettl, A, Shearing, PR, Harris, SJ, Brandon, NP, Schmidt, V. Stochastic simulation model for the 3d morphology of composite materials in Li‐Ion batteries. Comput Mater Sci 2011, 50:3365–3376.
Swendsen, RH, Wang, J‐S. Nonuniversal critical dynamics in Monte Carlo simulations. Phys Rev Lett 1987, 58:86–88.
Frisch, HL, Hammersley, JM, Welsh, DJ. Monte Carlo estimates of percolation probabilities for various lattices. Phys Rev 1962, 126:949–951.
Grimmett, G. Probability on Graphs: Random Processes on Graphs and Lattices. Cambridge, MA: Cambridge University Press; 2010.
Jerrum, M. Counting, Sampling and Integrating: Algorithms and Complexity. Basel, Switzerland: Birkhauser Verlag; 2003.
Lovász, L. Randomized algorithms in combinatorial optimization. DIMACS Ser Discrete Math Theor Comput Sci 1995, 25:153–179.
Mitzenmacher, M, Upfal, E. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge, MA: Cambridge University Press; 2005.
Motwani, R, Raghavan, R. Randomized Algorithms. Cambridge, MA: Cambridge University Press; 1997.
Rubinstein, RY, Ridder, A, Vaisman, R. Fast Sequential Monte Carlo Methods for Counting and Optimization. New York: John Wiley %26 Sons; 2014.
Boyle, P. Options: a Monte Carlo approach. J Financ Econ 1977, 4:323–338.
Giles, MB. Multilevel Monte Carlo path simulation. Oper Res 2008, 56:607–617.
McNeil, AJ, Frey, R, Embrechts, P. Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press/Princeton Series in Finance: Princeton, NJ; 2005.
Glasserman, P. Monte Carlo Methods in Financial Engineering. New York: Springer‐Verlag; 2004.
Gerstner, T, Kloeden, PE, eds. Recent Developments in Computational Finance: Foundations, Algorithms and Applications. Singapore: World Scientific; 2013.
Liu, JS. Monte Carlo Strategies in Scientific Computing. New York: Springer‐Verlag; 2001.
Efron, B, Tibshirani, R. An Introduction to the Bootstrap. New York: Chapman %26 Hall; 1994.
Geman, S, Geman, D. Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 1984, 6:721–741.
Gilks, WR, Richardson, S, Spiegelhalter, DJ. Markov Chain Monte Carlo in Practice. New York: Chapman %26 Hall; 1996.
Robert, CP, Casella, G. Monte Carlo Statistical Methods. 2nd ed. New York: Springer‐Verlag; 2004.
Brooks, S, Gelman, A, Jones, G, Meng, X‐L. Handbook of Markov Chain Monte Carlo. Boca Raton, FL: CRC Press; 2011.
Costa, A, Jones, OD, Kroese, DP. Convergence properties of the cross‐entropy method for discrete optimization. Oper Res Lett 2007, 35:573–580.
Goschin, S, Weinstein, A, Littman, M. The cross‐entropy method optimizes for quantiles. In: Proceedings of The 30th International Conference on Machine Learning 2013, 1193–1201.
Margolin, L. On the convergence of the cross‐entropy method. Ann Oper Res 2005, 134:201–214.
Kroese, DP, Porotsky, S, Rubinstein, RY. The cross‐entropy method for continuous multi‐extremal optimization. Method Comput Appl Probab 2006, 8:383–407.
Bucklew, JA. Introduction to Rare Event Simulation. New York: Springer‐Verlag; 2004.
Chan, JCC, Kroese, DP. Improved cross‐entropy method for estimation. Stat Comput 2012, 22:1031–1040.
de Boer, P‐T, Kroese, DP, Mannor, S, Rubinstein, RY. A tutorial on the cross‐entropy method. Ann Oper Res 2005, 134:19–67.
Dick, J, Pillichshammer, F. Digital Nets and Sequences. Discrepancy Theory and Quasi‐Monte Carlo Integration. Cambridge, MA: Cambridge University Press; 2010.
Dick, J, Kuo, FY, Peters, GW, Sloan, IH. Monte Carlo and Quasi‐Monte Carlo Methods 2012. New York: Springer-Verlag; 2014.
Niederreiter, H. Random Number Generation and Quasi‐Monte Carlo Methods. Philadelphia, PA: SIAM; 1992.

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