Monte Carlo Simulation Error Propagation
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Error Propagation Physics
Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; error propagation excel it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top uncertainties from Monte Carlo simulation and error propagation are different up vote 0 down vote favorite Inspired by this post Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?, gaussian error propagation calculator I try to check it myself using a simple function f=A/B, where A is 10 with uncertainty 1 and B is 5 with uncertainty 2. The error of f from error propagation is 0.6, however, the error of f from Monte Carlo simulation is 221.5. I'm very confused why this happens. I attached my code below: > runs = 100000 > A=10 > sigmaA=1 > B=5 > sigmaB=2 > simA <- rnorm(runs,mean=meanA,sd=sigmaA) > simB <- rnorm(runs,mean=meanB,sd=sigmaB) > f=A/B > f [1] 2 > sigmaf=sqrt(f^2*((sigmaA/A)^2+(sigmaB/B)^2-2*sigmaA*sigmaB/A/B)) > sigmaf [1] 0.6 > simf=simA/simB > sd(simf) [1] 221.5475 Thank you for your help! r monte-carlo error-propagation share|improve this question asked Mar 9 at 19:22 yuqian 36615 1 First of all, your formula for the error propagation is not correct. Instead of sigmaA*sigmaB it should be sigmaAB, i.e., the covariance between A and B, which is zero here. Then you should consider the last sentence there. If I correct the calculation of sigmaf to sigmaf <- abs(f) * sqrt(((sigmaA/A)^2+(sigmaB/B)^2)) and change sigmaB to 0.5, I get a good agreement between both estimates. –
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Error Propagation Correlated Variables
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Abstract Export Advanced search Close This document does not have an outline. JavaScript is disabled on your browser. Please enable JavaScript to use all the features http://stats.stackexchange.com/questions/200825/uncertainties-from-monte-carlo-simulation-and-error-propagation-are-different on this page. Computers & Chemistry Volume 8, Issue 3, 1984, Pages 205-207 A monte-carlo approach to error propagation Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by using the show more link. Opens overlay J.F. Ogilvie 1 Research School of Chemistry, Institute of Advance Studies, http://www.sciencedirect.com/science/article/pii/0097848584800078 The Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia Received 21 October 1983, Available online 9 January 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:10.1016/0097-8485(84)80007-8 Get rights and content AbstractA Monte-Carlo approach to error propagation from input parameters of known variance (and covariance if available) properties through an arbitrarily complicated analytic or numerical transformation to output parameters is discussed. A simple random-number generator for a rectangular distribution function is shown to provide an econimical and fairly efficient means of simulating the effects of using a normal distribution function. open in overlay 1Present address: Department of Physics, University of Albama, AL 35486-1921, U.S.A. Copyright © 1984 Published by Elsevier Ltd. ElsevierAbout ScienceDirectRemote accessShopping car
jot down some of my experiences with teaching error propagation. Right off the bat I should note that I have been greatly influenced by this document by John Denker in response to questions about this topic on the https://arundquist.wordpress.com/2011/06/27/error-propagation/ PHYS-L listserv. I especially like his rant against significant figures in that document, but I'll let that go for now. I'd like to talk about how I encourage the high school teachers in my licensure program to do and teach error propagation. I don't do the calculus method because, um, it requires calculus and students get bogged down in that instead of the important stuff (things like with error propagation comments like "I guess I messed up the calculus" vs and comments like "wow, this is a really accurate measurement" with the Montecarlo method). Before I forget, here's the calculus method. Assume you've measured a, b, and c with their associated errors and . Now you want to calculate some crazy function, f, of all the variables, or f(a, b, c). The error on f (assuming no correlations among error propagation calculator the variables) is given by: You can see why it's a hassle, what with the partial derivatives and all the terms to keep track of. One (of many) nice things about it is how you can quickly see which variable you should spend money on. Montecarlo method The Montecarlo method uses a computer to do many simulations of the experiment, where the variables are all randomly selected to be close to the best measurement you make. Specifically, you create several normally distributed (assuming that's the distribution of your data - a common case) random numbers that resemble the original data set. You then let the computer calculate the formula of interest several times over and then take the average and standard deviation of those to determine the best estimate of the function and the error on the function. I encourage students to do this with spreadsheets. Each column is a variable measured in class. Then you add a column for any calculations that you care to do with that data. You use a command to generate the random numbers, stretch the formulas down a few 100 or 1000 rows, and then use the typical Average and Stdev commands on the columns you care about. F
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