Monte Carlo Error Propagation
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Error Propagation Physics
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Error Propagation Chemistry
have an outline. JavaScript is disabled on your browser. Please enable JavaScript to use all the features 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 error propagation square root 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, 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-num
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Error Propagation Reciprocal
Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags error propagation inverse Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, propagated error calculus data mining, and data visualization. Join them; 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 http://www.sciencedirect.com/science/article/pii/0097848584800078 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?, 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. http://stats.stackexchange.com/questions/200825/uncertainties-from-monte-carlo-simulation-and-error-propagation-are-different 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. –Roland Mar 11 at 9:11 1 Possible duplicate of Propagation of large errors –Roland Mar 11 at 9:16 Hi Roland, Thanks! Now I understand that I made two mistakes. One is that I misunderstand sigmaAB, and the other is that I propagate large errors, which is explained clearly in the post you mention. Thank you so much! –yuqian Mar 13 at 18:43 add a comment| active oldest votes Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook. Your Answer
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings http://stats.stackexchange.com/questions/189111/monte-carlo-error-propagation and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags 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; it only error propagation 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 Monte Carlo error propagation up vote 1 down vote favorite Consider a set $X$ of $N$ iid random variables, each one with its own standard deviation: $$X: \{x_1\pm\sigma_1, x_2\pm\sigma_2, ..., x_N\pm\sigma_N\}$$ Say I have monte carlo error a "black box" numerical function which only accepts the means of each variable, ie: $\{x_1, x_2, ..., x_N\}$. This function outputs a single value, which I call $y_{m}$. The black box is not able to use the standard deviations of each variable in the $X$ set to estimate the uncertainty associated with $y_m$. But I need to estimate an uncertainty for $y_m$. I thus apply a Monte Carlo process in this way: Draw a random value for each variable in the $X$ set, assuming a normal distribution with mean $x_i$ and standard deviation $\sigma_i$. This generates a new "random set" $X_1$. Process $X_1$ with the black box, and store the result: $y_{1}$. Repeat points 1. and 2. $M$ times. The result is a set $Y$ of $M$ "black box values": $Y:\{y_1, y_2, ..., y_M\}$ Calculate the mean and standard deviation of $Y$: $\bar{y}\pm\sigma_y$. My understanding of this process is that for a large enough $M$ then $\bar{y}\to y_m$ and $\sigma_y$ can be assigned as the standard deviation of $y_m$. Is this assumption correct? Add: Can I assign $\sigma_y$ as the standard devia