Monte Carlo simulacija
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Monte-Carlo metode su stohastičke (determinističke) simulacijske metode, algoritmi koji s pomoću slučajnih ili kvazislučajnih brojeva i velikog broja izračuna i ponavljanja predviđaju ponašanje složenih matematičkih sustava.
Izvorno su osmišljene u državnom laboratoriju SAD u Los Alamosu nedugo nakon Drugog svjetskog rata. Prvo je elektroničko računalo u SAD-u upravo bilo dovršeno, i znanstvenici u Los Alamosu su razmatrali kako da ga najbolje iskoriste za razvoj termonuklearnog oružja (hidrogenske bombe). Kasne 1946. Stanislav Ulam je predložio korištenje slučajnog uzorkovanja za simuliranje putanja neutrona, a John von Neumann je razvio detaljan prijedlog rane 1947. Ovo je dovelo do simulacija manjih razmjera koje su ipak bile neophodno važne za uspješno dovršenje projekta. Metropolis i Ulam su 1949. objavili rad u kojem su iznijeli svoje ideje, čime su potaknuta velika istraživanja tokom 1950-ih godina. Metoda je dobila naziv po gradu u državici Monako, slavnom po svojim kockarnicama (što je prihvaćeno na prijedlog Nicka Metropolisa, jednog od pionira Monte-Carlo metode).
U ekonomiji se rabe ze proračunavanje poslovnog rizika, promjena vrijednosti investicija, pri strateškom planiranju i slično.
U medicinskoj fizici i radioterapiji koristi se za planiranje doze zračenja tumora.
Literatura
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- Eckhardt, Roger (1987). „Stan Ulam, John von Neumann, and the Monte Carlo method”. Los Alamos Science, Special Issue (15): 131–137.
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- Kahneman, D.; Tversky, A. (1982). Judgement under Uncertainty: Heuristics and Biases. Cambridge University Press.
- Kalos, Malvin H.; Whitlock, Paula A. (2008). Monte Carlo Methods. Wiley-VCH. ISBN 978-3-527-40760-6.
- Kroese, D. P.; Taimre, T.; Botev, Z.I. (2011). Handbook of Monte Carlo Methods. New York: John Wiley & Sons. str. 772. ISBN 0-470-17793-4.
- MacGillivray, H. T.; Dodd, R. J. (1982). „Monte-Carlo simulations of galaxy systems”. Astrophysics and Space Science (Springer Netherlands) 86 (2). [mrtav link]
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- Metropolis, N. (1987). „The beginning of the Monte Carlo method”. Los Alamos Science (1987 Special Issue dedicated to Stanislaw Ulam): 125–130.
- Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.; Teller, Augusta H.; Teller, Edward (1953). „Equation of State Calculations by Fast Computing Machines”. Journal of Chemical Physics 21 (6): 1087. Bibcode 1953JChPh..21.1087M. DOI:10.1063/1.1699114.
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- Sawilowsky, Shlomo S.; Fahoome, Gail C. (2003). Statistics via Monte Carlo Simulation with Fortran. Rochester Hills, MI: JMASM. ISBN 0-9740236-0-4.
- Sawilowsky, Shlomo S. (2003). „You think you've got trivials?”. Journal of Modern Applied Statistical Methods 2 (1): 218–225. [mrtav link]
- Silver, David; Veness, Joel (2010). „Monte-Carlo Planning in Large POMDPs”. u: Lafferty, J.; Williams, C. K. I.; Shawe-Taylor, J. i dr... Advances in Neural Information Processing Systems 23. Neural Information Processing Systems Foundation. Arhivirano iz originala na datum 2012-05-25. Pristupljeno 2015-06-16.
- Szirmay-Kalos, László (2008). Monte Carlo Methods in Global Illumination - Photo-realistic Rendering with Randomization. VDM Verlag Dr. Mueller e.K.. ISBN 978-3-8364-7919-6.
- Tarantola, Albert (2005). Inverse Problem Theory. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 0-89871-572-5.
- Vose, David (2008). Risk Analysis, A Quantitative Guide (Third izd.). John Wiley & Sons.
Vanjske veze
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- Hazewinkel Michiel, ur. (2001). „Monte-Carlo method”. Encyclopaedia of Mathematics. Springer. ISBN 978-1-55608-010-4.
- Overview and reference list, Mathworld
- Feynman-Kac models and particle Monte Carlo algorithms Arhivirano 2012-05-01 na Wayback Machine-u
- Introduction to Monte Carlo Methods Arhivirano 2012-08-09 na Wayback Machine-u, Computational Science Education Project
- The Basics of Monte Carlo Simulations Arhivirano 2012-08-30 na Wayback Machine-u, University of Nebraska-Lincoln
- Introduction to Monte Carlo simulation (for Microsoft Excel), Wayne L. Winston
- Monte Carlo Simulation for MATLAB and Simulink
- Monte Carlo Methods – Overview and Concept[mrtav link], brighton-webs.co.uk
- Monte Carlo techniques applied in physics Arhivirano 2016-03-04 na Wayback Machine-u
- Approximate And Double Check Probability Problems Using Monte Carlo method[mrtav link] at Orcik Dot Net
- Monte Carlo simulation using mathematica at Wolfram Mathematica
- Eric Grimson; John Guttag. „Lecture 20: Monte Carlo Simulations, Estimating pi”. Introduction to Computer Science and Programming stimating pi. MIT Open Courseware. Pristupljeno 4 February 2015.