# Questions tagged [error-propagation]

For questions on propagation of errors.

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### How can we use analysis to determine the error in computing a multidimensional function (Zorich)?

What is the relative error $\delta = \frac{|\Delta f|}{|f|}$ in computing the value of a function $f(x,y,z)$ at a point $(x,y,z)$ whose coordinates have absolute errors $\Delta x, \Delta y, \Delta z$? ...
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### How to measure the error between modeled and observed data?

Consider a scenario where observed data is represented in grey and modelled data in red, as below Here, the x-axis is a position, and the y-axis is an expected time, so that the slope defines, in a ...
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### Is there any way to compact the propagation of uncertainty formula in terms of vectors?

The uncertainty associated to $\xi=f(\mathbf x)$ with $\mathbf x\in\mathbf R^n$ is $$\delta\xi=\sqrt{\sum_{i=1}^n\left(\frac{\partial \xi}{\partial x_i}\delta x_i\right)^2}$$ What I was wondering was ...
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### Uncertainty propagation when using the Trapezium rule

I have some recorded data s(x), and need to compute the value and uncertainty in $$S = \int_{x_{1}}^{x_{2}} s(x) dx$$ I am using the trapezium rule for the integration, and need to estimate the ...
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### How do I go "backwards" with error propagation?

Hopefully this is appropriate for Math SE given that, ultimately, this questions stems from a math textbook (Zorich's Mathematical Analysis). Zorich has shown using simple arguments with absolute ...
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### Error Propagation in calculating Binary logarithm by hand

I am interested in the idea of arithmetic performed in binary done without electronics. In particular, I’d like to try calculating the binary logarithm of x (where 10 > x >= 1) using the square/...
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### Lop sided error due to non-negative data

I am currently working on a project where we are administering different treatments to subjects, but with some potential side effects. I am trying to measure the effect each method has on the well ...
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### Attributing error to each term through a product

I have a relatively straightforward problem. I have a value that gets multiplied by a bunch of correction factors to give a final answer. $Final = Base * CF_1 * CF_2 * CF_3 * CF_4$ I am trying to re-...
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### How to partially differentiate an equation with sums?

I'm working on a simple linear regression model in a physics course, where we are doing measurements of the round trip speed of light, over increasing distances. We are using the Least Squares method ...
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### How to find the margin of error of a value consisting of the sum of 5 values? [closed]

I have a $X$ value that is the sum of 5 different $x1,x2,x3,x4$, and $x5$ values. Eacn $x_i$ has their error in same scale. I want to calculate the error of X. How can i do that? Basically, i tried to ...
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### Find variance of random variable $W\cos\theta+L\sin\theta$ where $L,W,\theta$ are normal random variables. Uncertainty propagation problem.

I have three variables - these are length ($L$), width ($W$) and angle ($\theta$). Each has a known mean and variance. $\theta$ is independent, but $L$ and $W$ are correlated, and I know their ...
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### Difference between Absolute and Relative differences

I was reading a USACO Guide Page on data types and I came across two formulas for the absolute and relative difference in the desired answer and the actual answer that is outputted. This is meant to ...
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