For questions on propagation of errors.

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2answers
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Order of error of a fraction

If two functions can be written as the sum of some expression and an error term of higher orders of error $\epsilon$: $$f(x+\epsilon)=f_0(x,\epsilon)+O(\epsilon^m)\quad \text{ and} \quad ...
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1answer
480 views

Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in ...
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1answer
24 views

Relative Error $\frac{x-x_0}{x}$

According to many definitions I've seen the relative error is defined by $$E = \frac{x-x_0}{x}$$ where $x$ is the "true" value. But some people use instead $$\frac{x-x_0}{x_0}. $$ Is this incorrect? ...
2
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1answer
51 views

Help in Measuring Error on Estimates of Differential Equations

I am working on a project for class where I have to estimate the solutions to a damped harmonic oscillator ($x''+2 \gamma x'+ \omega^2 x=0$) and compare three methods for doing so (Third Order ...
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1answer
14 views

Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
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1answer
270 views

Calculating Covariance. (Multiplication of Two Covariance Matrices)

I have an equation T3=T1*T2 where T is 3*3 Transformation matrix representing position of an object in 3D. Now each of these position has some error in the form of 3*3 covariance matrix i-e ∑. My ...
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1answer
104 views

How is statistical uncertainty calculated for the modulus function?

I know it's an unusual function to calculate an uncertainty for, but I haven't been able to figure out a reasonable means for calculating derivatives for it to do so myself. I know modular arithmetic ...
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1answer
36 views

Statistical methods in experiments

I'm currently facing a huge problem in manipulating raw data from an experiment. Suppose I have the set of data: $$T_1=6.12 \pm 0.001s,\\ T_2=4.90875 \pm 0.001s, \\ T_3=3.9 \pm 0.001s, \\ T_4=3.69 ...
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1answer
36 views

Error propagation for ratio data

I'm working with some published ratio data for isotopes of uranium (238U) and lead (208Pb and 206Pb). The data are published in ratios of 238U/208Pb and 206Pb/208Pb, but I need the data to be in the ...
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1answer
80 views

Error bound of the Euler method

I am self studying working through the book "A First Course in the Numerical Analysis of Differential Equations" and have come to a deadend on q 1.2. The linear system $y' = Ay, y(0) = y_0$, where ...
2
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0answers
88 views

Accuracy of distance and bearing between GPS locations

I'm writing on an Android app that tracks the distance and bearing between two GPS location (each from a different device). Finding the mean distance and angle between the devices is quite easy, and ...
2
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0answers
52 views

Show that $\displaystyle\sum_{i=0}^{N-1}|\epsilon_i|\to0, N\to\infty$

Let $I_o=[t_0,t_0+T]\subset\mathbb R, T>0$, If $f\in C^0(I_0\times\mathbb R,\mathbb R)$ and satisfies the Lipschitz condition: $\forall t\in I_0, \forall y,y^{*}\in\mathbb ...
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0answers
40 views

Monte Carlo with error on individual samples

I'm performing a Monte Carlo integration where the individual samples have an error, and I'm wondering how to estimate the final error. Some more detail: The integral E I'm after is estimated in the ...
2
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0answers
40 views

Yacov Perelman Nepero game

This is my first question, so sorry if I'll make any mistake in using the site formatting. I found this game on a book by Yacov Perelman and I thought it could be nice to introduce Nepero number to ...
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0answers
14 views

To what set do measured values belong?

This question is more conceptual than practical. It seems that when we apply mathematics to measured values, we treat them like real numbers. When measured values take error into account using ± ...
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0answers
29 views

Calculating absolute error. Teacher distributes the abs value signs.

Ill illustrate my confusion with an example: It can be shown, assuming $E_xE_y=0$ that the error in an arithmetical multiplication will be: $E_{xy}=xE_y+yE_x+\mu$ Where $\mu$ is the so called ...
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0answers
20 views

Uncertainty in distance from uncertainty in coordinates

I know this is basic, but I've managed to get myself confused. So, I have an object at location $(x,y,z)$ with uncertainty in the location of $(\delta x, \delta y, \delta z)$. What is the ...
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0answers
46 views

Is the Taylor Expansion a good approximation

Say I use a computer to sum the first 26 terms of $e^{-5}$ (degree 25), will this taylor expansion provide a good approximation? It summed to $.0067$ To me this seems like a good approximation, but I ...
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0answers
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Link between total diffential and error caculation?

I earlier asked this question Error propagation, why use variences?. And am now slightly confused about the link between error propagation and total diffentials. As mentioned in the linked question, ...
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0answers
36 views

Accounting for drop-outs in clinical trials

'Physical Therapy Review' [Intention to treat analysis, compliance, drop-outs and how to deal with missing data in clinical research: a review Susan Armijo-Olivo, Sharon Warren and David Magee Faculty ...
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0answers
75 views

Expand $\int_{-1}^0 e^{a\cos{\theta}}J_0(b\sin{\theta})\,d\cos{\theta}$ in spherical harmonics.

I want to solve the integral (a probability density function) $$ g(\gamma)=\int_{-1}^0 e^{-f\cos{\theta}\cos{\gamma}}J_0(-if\sin{\theta}\sin{\gamma})\,d\cos{\theta} $$ numerically, everything is ...
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0answers
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Propagation of variance/covariance for $L_1$ Estimator with no analytic solution

This is my first question on Math Exchange so my apologies if it does not initially fit the format. I have a problem where I'd like to calculate the a-posteriori variance/covariance matrix of ...
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0answers
54 views

Finite difference method - implementation and stability

I have a PDE for a function $P(r,t)$ in spherical co-ordinates of the form $P_{t} = D(P_{rr} + (2/r)P_{r}) - a\Omega\left(\frac{P}{P + k} \right) $ where subscripts denote partial derivative with ...
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0answers
70 views

When examining global error bounds for Euler method, can I rescale the domain limits?

I'm looking at provable global error bounds of the Euler method for the first time and I was surprised to find that the bound grows exponentially in the amount of time (the domain size) propagated ...
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0answers
206 views

Problem Condition and Algorithm Stability

Consider 2 mathematical problems: $$ f_1(x) = a - x \\ f_2(x) = e^x -1 $$ The condition number for a function is defined as follows: $$ k(f) = \left| x \cdot \frac{f'}{f} \right| $$ Lets analyze ...
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0answers
60 views

How to estimate error pattern of a set of line segments with respect to given reference segments (2D case)

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I have been the reference data and then I extracted other line segments ...
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0answers
15 views

Measure of how well a 3D function represents experimental data

I have experimental data of a one dimensional heat equation and corresponding values for a predicted temperatures. Is there any method in which I could statistically analyse the data to determine if ...
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0answers
12 views

Error propagation with dependent errors

I have a function $f(x_1,\ldots,x_n)$ where the variables $x_k$ have errors $\delta_k$. If these errors are independent I can add them root mean square: $\delta ...
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0answers
11 views

low number poissonian errors: is it possible for a measurement of 4 counts to have a significance higher than 2 sigma?

What is the best way to measure statistical significance of an overdensity in counting experiment where you have small numbers? Rather than bore you with my actual problem, please consider the ...
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0answers
11 views

Error on determinant from statistical errors on complex matrix elements

Say I have a complex matrix $A$ whose elements $A_{ij}$ have statistical error $\delta_{ij}$. I need to figure out from these errors what will be the error on the determinant $|A|$. If the matrix was ...
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0answers
7 views

Propagating uncertainties in Gaussian fit

I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian ...
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0answers
19 views

Geometric Mean of Random Variables

I measure a series of $n$ objects [O_1, O_2, O_3, ..., O_n]. Because those measurements are quite hard to perform, I have quite a lot of measurement error and ...
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0answers
20 views

Statistical uncertainty on a percentages inferred from an A/B test

Question: What is the statistical uncertainty on percentages inferred from an A/B test? Example: $N = 100$ people are presented with an A/B choice (e.g., jumping into shark-infested water, choosing ...
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0answers
25 views

Error of 2 correlated variables, proxied as random variables

Disclaimer: my 1st question in math.stackexchange (usually in stackoverflow !), and non-English speaker. I'm trying to solve this problem for an arbitrary no. of variables, with multiple categories ...
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0answers
22 views

Is there a standard method in finding the maximum of the following?

This is an elementary level exercise in error estimation. The figure shows that, from a rectangular plate AXBYCDZF, another smaller rectangular plate EDZF is cut off. {$AB = a, BC = b, XB = p$ and ...
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0answers
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John Von Neumann Error distribution

I have a sort of general question. John Von Neumann proposed am error distribution function as following. $error = A*e^{ikx} $ with k: the wavenumber Now our professor asked us, why is it so ...
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0answers
15 views

Error propagation of non-square Matrix

I measure values of the vector $\vec{P}$ where each value $P_i$ has its own error $E_i$. I'm interested in the vector $\vec{K}$. Both values are linked by $\vec{K} = M \vec{P}$ . Since $\vec{P}$ and ...
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0answers
27 views

Looking for a motivating example for backward error analysis

For many people, it seems self-evident that backward error is a powerful tool in numerical analysis. But for me, it is hard to imagine a situation in which backward error analysis provides any useful ...
0
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0answers
51 views

Error propagation in pearson correlation

I have two data-sets $X$ and $Y$ with errors $\Delta X$ and $\Delta Y$. I calculated the Pearson Sample Correlation $r$. Is it possible to calculate the error of $r$ using propagation of uncertainty: ...
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0answers
23 views

How to find error constant, global and local error of ODE integration method

In literature regarding open channel flows I bumped into strange ODE integration methods: the first one: $$y_{i+1}=y_i+\Delta x\cdot\sqrt{f_i\cdot f_{i+1}}$$ the second one $$y_{i+1}=y_i+\Delta ...
0
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0answers
88 views

Error Propagation - functions of the mean.

Given a number of measurements $\{x_i\}$ with values distributed according to a (known) probability distribution $\rho(x)$ with a theoretical mean $\langle x\rangle = \int dx x\rho(x) = f(y)$ and a ...
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0answers
63 views

Propagation of standard deviation for random variable with Markov Property

I have a discrete random variable, $X \in \{0,1,2,3\}$. Define the indicator function: $$ 1_{k}\left(x\right) = \begin{cases} 1, & \text{if $x=k$} \\ 0, & \text{otherwise} \\ \end{cases}$$ ...