Error Propagation Correlation Matrix
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propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables error propagation correlated variables are the values of experimental measurements they have uncertainties due to
Covariance Matrix Error Propagation
measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function. The uncertainty u
Error Propagation Rules
can be expressed in a number of ways. It may be defined by the absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which
Error Propagation Calculator
is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, the positive square root of variance, σ2. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution of the variable is known or can error propagation physics be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability that the true value lies in the region x ± σ. If the uncertainties are correlated then covariance must be taken into account. Correlation can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 Caveats and warnings 2.3.1 Reciprocal 2.3.2 Shifted reciprocal 3 Example formulas 4 Example calculations 4.1 Inverse tangent function 4.2 Resistance measurement 5 See also 6 References 7 Further reading 8 External links Linear combinations[edit] Let { f k ( x 1 , x 2 , … , x n
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta error propagation chemistry Discuss the workings and policies of this site About Us Learn more error propagation square root about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross error propagation reciprocal 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 https://en.wikipedia.org/wiki/Propagation_of_uncertainty 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 What does correlation mean in error propagation? up vote 0 down vote favorite From the python uncertainties package: Correlations between expressions are correctly taken into http://stats.stackexchange.com/questions/139321/what-does-correlation-mean-in-error-propagation 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 [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 a
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