For questions on propagation of errors.

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3answers
62 views

How to calculate the standard deviation of numbers with standard deviations?

I have essentially a propagation-of-error problem I run into frequently with my scientific data. For example, I have three samples, each of which I take two measurements of. So, for each sample, I can ...
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2answers
36 views

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
431 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
17 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? ...
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1answer
118 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
74 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
6 views

Error Propagation of parameter in an irreversible equation

I have the following equation that predicts a certain parameter $c_t$: $$c_t = f(x,y_1,y_2,y_3...)$$ The function $f$ is known, continuous, real, differentiable to all arguments and the solution to a ...
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1answer
24 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
36 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
52 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 ...
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0answers
14 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 ...
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0answers
46 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
33 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 ...
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0answers
28 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
11 views

How to estimate variances for Kalman filter from real sensor measurements without underestimating process noise.

As the title says, I want to estimate the variances needed for a Kalman filter from real sensor measurements only. For example we can take a temperature sensor, but the solution shall be as ...
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0answers
24 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
49 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
27 views

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
48 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
65 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
180 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
55 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
9 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
7 views

Taylor approximation for roots of the quadratic equation

I am working on section 2.2, question 8 of Numerical Analaysis (Ward/Cheney) which asks me to find methods to avoid a loss of significance in the quadratic formula when 4ac is close to b^2. I have a ...
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0answers
17 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 ...
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0answers
32 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
17 views

How to express the quantity using significant figures to imply the stated error?

Express the quantity using significant figures to imply the stated error. $$1.77 \pm 0.06$$ I tried to factor out a $6$ and got $6(.295\pm0.01)$ but then when I try to make $.295$ have an error of ...
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0answers
14 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 ...
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0answers
22 views

what are some good ways to define the errors between two functions?

I have two functions. One is the original function (that contains 4 variables), and the second one is the approximation to the first one (also contains 4 variables). The question is, if I want to ...
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0answers
6 views

To find error in time histogram

I have a data which is recorded from a detector. Whenever the detector produce signal it records the time. I have recorded the data for several cycles, one cycle is 0 to 1 second. Finally I made the ...
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0answers
22 views

Monte carlo error: Combining “experimental” and statistical errors

I'm doing a slightly involved Monte Carlo approximation of a quantity $E$ where I end up with the following formula: $E=\frac{\sum_{i=1}^np_ie_iG_i}{\sum_{i=1}^np_iG_i}\ .\ \ \ \ \ \ \ \ \ $ (1) ...
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0answers
11 views

looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
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0answers
40 views

Standard deviation on absolute square of complex average

I am calculating a quantity $q=|c|^2$ where I obtain $c\in\boldsymbol C$ as an average of a collection of estimates with errors: $\langle c\rangle=\sum_{j=1}^nc_j$, and the question is what error to ...
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0answers
64 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
71 views

Numerical Error in Computation - What Are the Students' Expected to Know?

I'm going to conduct an educational research about math undergraduates' conceptions about "numerical error." So I'm making a list of items I think someone with a BSc in mathematics is expected to know ...
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0answers
50 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: $$ 1_{k}\left(x\right) = \begin{cases} 1, & \text{if $x=k$} \\ 0, & \text{otherwise} \\ \end{cases}$$ ...