1 / 10

Monte Carlo Simulation

Presented by: Zhenhuan Sui. Monte Carlo Simulation. Introduction From A Simple Application. 1. M. N. S=N/M. 1. Facts. It is the computational algorithm that rely on repeated random sampling to compute its result

mahlah
Download Presentation

Monte Carlo Simulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Presented by: Zhenhuan Sui Monte Carlo Simulation

  2. Introduction From A Simple Application 1 M N S=N/M 1

  3. Facts • It is the computational algorithm that rely on repeated random sampling to compute its result • Investigating radiation shielding and the distance that neutrons would likely travel through various materials at Los Alamos Scientific Laboratory in Manhattan Project • John von Neumann and Stanislaw Ulam: modeling the experiment on a computer using chance • The name is a reference to the Monte Carlo Casino in Monaco where Ulam's uncle would borrow money to gamble • 1950s’ hydrogen bomb

  4. General Steps For MCS • Define a domain of possible inputs • Generate inputs randomly from the domain using a certain specified probability distribution • Perform a deterministic computation using the inputs • Aggregate the results of the individual computations into the final result • suited to calculation by a computer • statistical simulation method • http://en.wikipedia.org/wiki/Monte_Carlo_method#Monte_Carlo_and_random_numbers

  5. Elements • probability density function • random number generator • sampling rules • simulation results • uncertainties estimation • technology to reduce the variance

  6. Buffon's Needle The uniform probability density function of x between 0 and t /2 is 2/t dx The uniform probability density function of θ between 0 and π/2 is 2/π d θ http://upload.wikimedia.org/wikipedia/commons/f/f6/Buffon_needle.gif http://en.wikipedia.org/wiki/Buffon%27s_needle

  7. Further For π http://en.wikipedia.org/wiki/Buffon%27s_needle

  8. Steps For Applications • based on the properties of the systems we want to solve, we construct the theoretical models which can describe the properties. • try to get the probability density functions of some properties for the models. • From the probability density functions, we can produce some random samplings and get some simulation results. • analyze the results and do predictions for some properties of the systems.

  9. Applications • Physics: • quantum chromodynamics • statistical physics • particle physics • Mathematics: • Monte Carlo integration: algorithms for the approximate evaluation of definite integrals, multidimensional ones • numerical optimization • Finance and business: • calculate the value of companies • evaluate investments in projects • evaluate financial derivatives • risk management, there would be a lot of variables in the equations • Quasi-Monte Carlo methods in finance

  10. http://en.wikipedia.org/wiki/Monte_Carlo_method#Finance_and_businesshttp://en.wikipedia.org/wiki/Monte_Carlo_method#Finance_and_business http://en.wikipedia.org/wiki/Monte_Carlo_method http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_methods_in_finance http://baike.baidu.com/view/7775.html http://www.virtualphantoms.org/egs4/temp/mchome.htm http://www.linuxsir.org/bbs/thread288992.html Resources

More Related