Correlation Error Propagation
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Propagation Of Error Division
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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 What does correlation mean in error error propagation square root propagation? up vote 0 down vote favorite From the python uncertainties package: Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a non-zero uncertainty for x-x, which is incorrect). x is a single value, with an uncertainty. What does correlation mean in this context? Example code to illustrate what it's talking about: In [1]: from uncertainties import ufloat, umath In [2]: x = ufloat(2,1) In error propagation chemistry [3]: x Out[3]: 2.0+/-1.0 In [4]: y = ufloat(2,1) In [5]: y Out[5]: 2.0+/-1.0 In [6]: z = umath.log(umath.exp(x)) In [7]: z Out[7]: 2.0+/-1.0 In [8]: x-y Out[8]: 0.0+/-1.4142135623730951 In [9]: x-z Out[9]: 0.0+/-0 In this example, x, y, and z are all single values with an uncertainty. I don't understand how two single values can be "correlated". In a practical sense, I'd also be interested to know how uncertainties actually keeps track of this "correlation". Further, why doesn't this include some of the uncorrelated error between x and z? In [10]: b=x+y In [11]: c=y+z In [12]: b-c Out[12]: 0.0+/-0 correlation error-propagation probability-calculus share|improve this question edited Feb 26 '15 at 4:10 asked Feb 25 '15 at 22:36 naught101 1,8282454 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote accepted $x$ is perfectly correlated with itself, so $x-x$ is $0$, with no uncertainty. The example given in the documentation is not really a very good one, since this isn't a common situation and the result is trivial. More importantly, if $x$ and $y$ are correlated, than the documentation is claiming that the code will take this correlation into account when computing an uncertainty for $x-y$. The OP edited his question, so I've edited this response to try to answer the new question: In this code, $x$, $y$, and $z$ are random variables with given expected values, s