Monte Carlo Error Analysis
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that we use for the average. A possible measure of the error
What Is Monte Carlo Error
is the ``variance'' defined by: (269) where and The monte carlo standard error ``standard deviation'' is . However, we should expect that the error decreases with
Monte Carlo Error Definition
the number of points , and the quantity defines by (271) does not. Hence, this cannot be a good measure of the error. monte carlo standard error definition Imagine that we perform several measurements of the integral, each of them yielding a result . Thes values have been obtained with different sequences of random numbers. According to the central limit theorem, these values whould be normally dstributed around a mean . Suppouse that monte carlo error propagation we have a set of of such measurements . A convenient measure of the differences of these measurements is the ``standard deviation of the means'' : (270) where and Although gives us an estimate of the actual error, making additional meaurements is not practical. instead, it can be proven that (271) This relation becomes exact in the limit of a very large number of measurements. Note that this expression implies that the error decreases withthe squere root of the number of trials, meaning that if we want to reduce the error by a factor 10, we need 100 times more points for the average. Subsections Exercise 10.1: One dimensional integration Exercise 10.2: Importance of randomness Next: Exercise 10.1: One dimensional Up: Monte Carlo integration Previous: Simple Monte Carlo integration Adrian E. Feiguin 2009-11-04
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Monte Carlo Method
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Monte Carlo Simulation Excel
Advanced search Close This document does not have an outline. JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. http://www.northeastern.edu/afeiguin/phys5870/phys5870/node71.html Journal of Computational Physics Volume 126, Issue 2, July 1996, Pages 434-448 Regular ArticleStatistical Error Analysis for the Direct Simulation Monte Carlo Technique Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by using the show more link. Opens overlay Gang Chen, Opens overlay Iain D. Boyd http://www.sciencedirect.com/science/article/pii/S0021999196901485 Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, 14853 Received 21 April 1995, Revised 5 February 1995, Available online 19 April 2002 Show more Choose an option to locate/access this article: Check if you have access through your login credentials or your institution. Check access Purchase Sign in using your ScienceDirect credentials Username: Password: Remember me Not Registered? Forgotten username or password? OpenAthens login Login via your institution Other institution login doi:10.1006/jcph.1996.0148 Get rights and content AbstractThe statistical error associated with the direct simulation Monte Carlo technique is studied when it is applied to nonequilibrium hypersonic and nozzle flows. A root mean square (rms) error is employed as an indicator of the level of the statistical fluctuations. The effects of number of particles per cell and sample size are analyzed and quantified. It is found that in order to adequately model the physics of interest, the number of particles in the simulation must be greater than a certa
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