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

• Anderson, Herbert L. (1986). „Metropolis, Monte Carlo and the MANIAC”. Los Alamos Science 14: 96–108. 
• Baeurle, Stephan A. (2009). „Multiscale modeling of polymer materials using field-theoretic methodologies: A survey about recent developments”. Journal of Mathematical Chemistry 46 (2): 363–426. DOI:10.1007/s10910-008-9467-3. 
• 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. 
• Binder, Kurt (1995). The Monte Carlo Method in Condensed Matter Physics. New York: Springer. ISBN 0-387-54369-4. 
• Caflisch, R. E. (1998). Monte Carlo and quasi-Monte Carlo methods. Acta Numerica. 7. Cambridge University Press. str. 1–49. 
• Davenport, J. H.. „Primality testing revisited”. Proceeding ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation: 123 129. DOI:10.1145/143242.143290. ISBN 0-89791-489-9. 
• Doucet, Arnaud; Freitas, Nando de; Gordon, Neil (2001). Sequential Monte Carlo methods in practice. New York: Springer. ISBN 0-387-95146-6. 
• Eckhardt, Roger (1987). „Stan Ulam, John von Neumann, and the Monte Carlo method”. Los Alamos Science, Special Issue (15): 131–137. 
• Fishman, G. S. (1995). Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer. ISBN 0-387-94527-X. 
• C. Forastero and L. Zamora and D. Guirado and A. Lallena (2010). „A Monte Carlo tool to simulate breast cancer screening programmes”. Phys. In Med. And Biol. 55 (17): 5213–5229. Bibcode 2010PMB....55.5213F. DOI:10.1088/0031-9155/55/17/021. 
• Golden, Leslie M. (1979). „The Effect of Surface Roughness on the Transmission of Microwave Radiation Through a Planetary Surface”. Icarus 38 (3): 451–455. Bibcode 1979Icar...38..451G. DOI:10.1016/0019-1035(79)90199-4. 
• Gould, Harvey; Tobochnik, Jan (1988). An Introduction to Computer Simulation Methods, Part 2, Applications to Physical Systems. Reading: Addison-Wesley. ISBN 0-201-16504-X. 
• Grinstead, Charles; Snell, J. Laurie (1997). Introduction to Probability. American Mathematical Society. str. 10–11. 
• Hammersley, J. M.; Handscomb, D. C. (1975). Monte Carlo Methods. London: Methuen. ISBN 0-416-52340-4. 
• Hartmann, A.K. (2009). Practical Guide to Computer Simulations. World Scientific. ISBN 978-981-283-415-7. 
• Hubbard, Douglas (2007). How to Measure Anything: Finding the Value of Intangibles in Business. John Wiley & Sons. str. 46. 
• Hubbard, Douglas (2009). The Failure of Risk Management: Why It's Broken and How to Fix It. John Wiley & Sons. 
• 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). 
• MacKeown, P. Kevin (1997). Stochastic Simulation in Physics. New York: Springer. ISBN 981-3083-26-3. 
• 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. 
• Metropolis, N.; Ulam, S. (1949). „The Monte Carlo Method”. Journal of the American Statistical Association (American Statistical Association) 44 (247): 335–341. DOI:10.2307/2280232. JSTOR 2280232. PMID 18139350. 
• M. Milik and J. Skolnick (Jan 1993). „Insertion of peptide chains into lipid membranes: an off-lattice Monte Carlo dynamics model”. Proteins 15 (1): 10–25. DOI:10.1002/prot.340150104. PMID 8451235. 
• Mosegaard, Klaus; Tarantola, Albert (1995). „Monte Carlo sampling of solutions to inverse problems”. J. Geophys. Res. 100 (B7): 12431–12447. Bibcode 1995JGR...10012431M. DOI:10.1029/94JB03097. 
• P. Ojeda and M. Garcia and A. Londono and N.Y. Chen (Feb 2009). „Monte Carlo Simulations of Proteins in Cages: Influence of Confinement on the Stability of Intermediate States”. Biophys. Jour. (Biophysical Society) 96 (3): 1076–1082. Bibcode 2009BpJ....96.1076O. DOI:10.1529/biophysj.107.125369. 
• Int Panis L; De Nocker L, De Vlieger I, Torfs R (2001). „Trends and uncertainty in air pollution impacts and external costs of Belgian passenger car traffic International”. Journal of Vehicle Design 27 (1–4): 183–194. DOI:10.1504/IJVD.2001.001963. 
• Int Panis L, Rabl A, De Nocker L, Torfs R (2002). P. Sturm. ur. „Diesel or Petrol ? An environmental comparison hampered by uncertainty”. Mitteilungen Institut für Verbrennungskraftmaschinen und Thermodynamik (Technische Universität Graz Austria) Heft 81 Vol 1: 48–54. 
• Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (1996) [1986]. Numerical Recipes in Fortran 77: The Art of Scientific Computing. Fortran Numerical Recipes. 1 (Second izd.). Cambridge University Press. ISBN 0-521-43064-X. 
• Ripley, B. D. (1987). Stochastic Simulation. Wiley & Sons. 
• Robert, C. P.; Casella, G. (2004). Monte Carlo Statistical Methods (2nd izd.). New York: Springer. ISBN 0-387-21239-6. 
• Rubinstein, R. Y.; Kroese, D. P. (2007). Simulation and the Monte Carlo Method (2nd izd.). New York: John Wiley & Sons. ISBN 978-0-470-17793-8. 
• Savvides, Savvakis C. (1994). „Risk Analysis in Investment Appraisal”. Project Appraisal Journal 9 (1). DOI:10.2139/ssrn.265905. 
• 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. 
• 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

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, 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 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.