# Questions tagged [error-propagation]

For questions on propagation of errors.

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### Optimize rank order survey experiment

What are methods for describing/comparing rank ordering of many items by multiple evaluators, where evaluators might not have the same items they are evaluating? For example: Suppose I have a dog show ...
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### Error on the Bin of a Normalised Histogram

Suppose I have a histogram, $N$, each with bins of width $\Delta x$, denoted by bin indices, $i$. The count of a single bin is then $N_{i}$. I wish to estimate the empirical density for a certain bin. ...
0answers
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### How is SVD better than Gaussian elimination in finding the rank of a matrix?

In Linear Algebra and its Applications, Gilbert Strang, $4^{th}$ ed, one of the applications of SVD is mentioned as finding the effective rank of a matrix. The idea presented in the book is that the ...
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### How to pick the axes and the method of linear regression?

I have to make a linear regression in two set of data $x_1,...,x_n$ and $y_1,...,y_n$, with standard deviations $\sigma_{x_1} = ... = \sigma_{x_n}$ and $\sigma_{y_1} \neq ... \neq \sigma_{y_n}$, and I ...
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### Backward Error Analysis : Determining Errors on Model's Inputs with Known Output Errors

I have an algorithm that takes 5 input parameters $r, i, \Omega, \omega, f$ and returns two outputs $X$ and $Y$. I happen to know the errors $\Delta X$, $\Delta Y$ associated to $X$ and $Y$ (which ...
1answer
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### Count users with big space between pings logic

please try to be lenient with me because I really have forgotten most of the stuff, so I will probably be making incorrect assumptions, word the problem incorrectly, etc. Context I'm trying to ...
0answers
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### Error Propagation on Orbital Elements through Non Linear Relation

I'm having a hard time trying to propagate errors for my current work. I have two known positions $X$ and $Y$ that depend on several orbital parameters $r, i, \Omega, \omega, f$ ($r$ is a distance ...
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### Propagation of large uncertainties

Unfortunately the error propagation formula breaks down for large errors e.g. $\sigma \approx \mu$ for a gaussian distribution, since it is derived under the assumption of small errors using a Taylor ...
0answers
19 views

### Question about error analysis for a normally distributed data

Let us suppose we have one constant variable $b \pm \delta b = 20 \pm 1$ and one function that depends on $x$, such as, $a(x) \pm \delta a$ The problem is I want the difference between $a(x)$ and $b$ ...
1answer
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### How to relate $|\delta x|$ and $|\tilde\delta x|$ in an inequality $A\le |\tilde\delta x|\le B$ where $A$ and $B$ contain $|\delta x|$?

$|\delta x| = |(\tilde x - x)/x|$ (this is the absolute value of relative error) $|\tilde\delta x| = |(\tilde x - x)/\tilde x|$ (bound for some distinct quantity) I need to find an inequality which ...
2answers
49 views

### Error propagation of a variable for an integral

I have an integral that depends on two parameters $a\pm\delta a$ and $b\pm \delta b$. I am doing this integral numerically and no python function can calculate the integral with uncertainties. So I ...
1answer
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### derivate is based on addition, is there a muliplication analogon?

like $$\operatorname{f^o}(x) = \lim_{h\to 1} \frac{f(x*h)}{f(x)}$$ $$\operatorname{f}(x)=e^x$$ $$\operatorname{f^o}(x) = \lim_{h \to 1} e^{x*h}/e^{x} = \lim_{h\to 1} e^{x*h-x}=e^0=1$$ does it ...
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### Solving a special rational equation on a very small interval

I need to solve the following equation (for $x$): \begin{equation} \mathcal f(x):=\sum_{i=1}^n b_i \left( \frac{a_i}{1+b_i x}\right)^2-\phi=0, \quad \text{with} \quad -1/b_1< x \le 0. \end{...
1answer
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### Which of the following lines offers the better fit to the given points in the least-squares?

I have two similar exercises: Which of the following lines, $y = 1 - x$ or $y = 4 - x$, offers the better fit to the points $(1,2),(2,1), (3,1)$ in the least-squares? Justify? My thought process (...
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19 views

### error on evaluation of line fit at a given x given error on its parameters

Say I have some data points randomly distributed about a linear model. I fit a straight line through it, and obtain best fit parameters $m$ and $b$ with an error $\delta_m$ and $\delta_b$ associated ...
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### The trapezoid rule has been used to approximate $\int_{2.3}^{3.1}f(x)dx$, find the maximum absolute error

A previous exercise was Determine $\int_{2.3}^{3.1}f(x)dx$ using the trapezoid rule. I got $0.452557$. Knowing that $E(f) =−h^2(b−a)f′′(η)/12$ with 2.3≤η≤3.1 gives the error of integration of the ...
1answer
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### How do you propagate uncertainty for the equation $\sqrt{\left( \frac{2 \sin{\theta}}{\sqrt{3}}+\frac{1}{2} \right)^{2}+\frac{3}{4}}$

I am calculating $n(\theta) = \sqrt{\left( \frac{2 \sin{\theta}}{\sqrt{3}}+\frac{1}{2} \right)^{2}+\frac{3}{4}}$. But I have a problem as $n = 59.96 \pm 0.01$. I have tried using a first order Taylor ...
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### Why I am getting this slight deviation

I have solved this equation by two method √3a = 50+a Method 1 √3a-a =50 a(√3-1) = 50 a= 50/(√3-1) a= 50/0.73 = 68.4 Method 2 a(√3-1) = 50 a = 50/(√3-1) a =50(√3+1)/2. [by rationalizing] a =25 * ...
0answers
20 views

### How to calculate measurement uncertainty for a derived function in respect to data set?

I have a self made pressure sensor for which i am trying to calculate the measurement uncertainty. Im trying to measure Force (in Newtons [N]) and have a +/- ...N result. The Sensor changes its ...
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### epidemiology and double exponential sigmoid, error bars.

I'm creating a model of the coronavirus in various countries using a combination of a double exponential sigmoid with the SIRD compartmental model. I'm getting some consistent results, but I'm not ...
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39 views

### Standard Error propagation for correlated variables

The following is a toy problem to illustrate my question. Let $[A_{1}, ... ,A_{n}]$ be a series of $n$ random variables. Each variable has $m$ observation under two experimental conditions resulting ...
3answers
113 views

### Forward and centered finite difference give same error plot: why?

Let us consider the following standard approximations of the first derivative of a function $$FD = \frac{f(x+h)-f(x)}{h}$$ $$CFD = \frac{f(x+h)-f(x-h)}{2h}$$ The first is first order accurate, while ...
1answer
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### Roundoff errors and finite difference approximation

Let us consider the centered finite difference approximation of the first derivative of a smooth function $$f'(x_i) = \frac{f(x+h) - f(x-h)}{2h}$$ It's well known that if we do a $\text{loglog}$ plot ...