Monte Carlo simulacija

Upotreba Monte Carlo metode u određivanju približne vrijednosti π. Nakon postavljanja 30000 slučajnih točaka, procjena za π je unutar 0.07% od stvarne vrijednosti. To se dešava s približnom vjerojatnošću od 20%.

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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  • Berg, Bernd A. (2004). Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code). Hackensack, NJ: World Scientific. ISBN 981-238-935-0. 
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  • 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. 
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  • Vose, David (2008). Risk Analysis, A Quantitative Guide (Third izd.). John Wiley & Sons. 

Vanjske veze

Monte Carlo simulacija na Wikimedijinoj ostavi
  • 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.