For questions on propagation of errors.

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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 $\mid A\mid$. If the ...
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1answer
474 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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28 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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6 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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18 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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19 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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1answer
12 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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18 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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3answers
297 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
30 views

How can I calculate the uncertainty of two combined uncertainties?

If uncertainty can be calculated as half the range, and percentage uncertainty is the uncertainty over a mean all multiplied by 100, how can I find what the uncertainty is of A^2 * B^3 when A = 21.3 ...
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2answers
43 views

Prove that the rounding error can contaminate half the digits of computed root

I am trying to resolve the following problem: If $b^2 \approx 4ac $ the rounding error can contaminate half the digits of the root computed with the formula: $\dfrac {-b \pm \sqrt {b^2 - 4ac}} ...
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1answer
42 views

Prove graphically that the Lambert equation has exactly zero, one or two roots

I need some help on the below problem. Consider the Lambert equation: $xe^x = a$ for real values of x and a (a) Show graphically that the equation has exactly one root $ \xi(a) \ge 0 $ if $ ...
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1answer
24 views

How does one bound computational error for a finite difference approximation of the second derivative?

I'm trying to wrap my head around ways to minimize total computational error (defined as a sum of the bounds on the truncation and rounding errors) by taking a differentiable function $f : \mathbb{R} ...
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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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23 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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1answer
22 views

How to show the relative error of $ \frac{x_A}{y_A}$

First, this is how the relative error of $x_Ay_A$ (approximated errors) is computed as compared to $x_Ty_T$ (true errors) - $ \displaystyle Rel(x_Ay_A) = \frac{x_Ty_T - x_Ay_A}{x_Ty_T}$, Letting ...
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21 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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20 views

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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45 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
20 views

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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1answer
44 views

Error propagation, why use variences?

I have been reading up on error propagation and am slightly confused about something. We can the error in $c=f(a,b)$ as the: $$\sigma(c)= f_a \sigma_a+f_b \sigma _b$$ Firstly is this correct and am I ...
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578 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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1answer
30 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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0answers
81 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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2answers
27 views

Absolute error in machine-precision terms.

I am trying to wrap my head around errors in floating point calculations. Let me denote absolute error as follows: $e = |x - \hat{x}|$, where $x$ is the exact number and $\hat{x}$ is its floating ...
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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? ...
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3answers
520 views

Calculate uncertainty of sine function result

I have an angle given in degrees: $$\theta_{\min} = 63^{\circ} \pm 0.5^{\circ}$$ I need to calculate it's sine and still know the uncertainty of the value: $$n = 2\sin(\theta_{\min}) = ...
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1answer
103 views

Stopwatch Accuracy and Precision

Let's say I have a stopwatch that can take split times. It's resolution is 1/100th of a second. Let's also say I have a robot that can press the split button exactly 0.244s apart in real time. I have ...
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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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74 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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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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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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1answer
145 views

Relative error % of cos and sin functions?

I've been searching all over the net and I can't seem to find a definitive answer - perhaps I'm asking the wrong question. How does one calculate the relative error (%) of the cos/sin/tan of an angle ...
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1answer
45 views

Sum of positive integers estimating sum of fractions

Given $m$ fractions adding up to an positive integer $n$ For example: $m=3\\n=10=\frac{30}{6}+\frac{20}{6}+\frac{10}{6}$ How can we find $m$ positive integers that sum to $n$ (a partition of $n$), ...
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1answer
26 views

Statistics on discrete probability with error?

I need help with this question, am pretty confused on what to do with the error, I can't see how to use it.
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26 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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49 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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1answer
275 views

Error Estimation and Propagation through Trigonometric Functions

I have a problem whereby I have to estimate the absolute error of a value calculated using values read from sensors. The equation used to calculate the value is $T_{xy} = R \tan \theta$. The sensor ...
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2answers
45 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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2answers
123 views

Regression with error coming from rounding

I am looking at the following model: $c$ is a fixed vector in $\mathbb{R}_+^n$ and for any $x \in \mathbb{R}_+^n$ we obtain a value $y =[c^Tx]$, i.e. rounding $c^Tx$ to the nearest integer. I want ...
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680 views

What is the error in calculated volume of cylinder, given the measurements of length and radius?

Measured length of the rod is $15 \pm 0.4$ cm and the radius of the rod is $6.1 \pm 0.2$ cm. What is the error in calculated volume? (two decimal places) What i've tried is $$V=\pi r^2 l$$ ...
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1answer
356 views

How to calculate uncertainties?

A question requires me to make a calculation involving variables with uncertainties, giving my answer with its result uncertainty. How do I do that?
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1answer
205 views

Drove 238 miles and used 27.3 litres of petrol: find upper bound for consumption per mile, considering measurement errors

X drove 238 miles, correct nearest mile. They used 27.3 litres of petrol, to the nearest tenth of a litre. $Petrol Consumption =$${Miles}\over Petrol Used$ Work out the upper bound. I used ...
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1answer
53 views

Uncertainty in measurements: if $x$ has uncertainty $\pm\epsilon$, what is the uncertainty in $\sin x$?

I have two questions regarding uncertainties in measurements. First, if I have some measured value for $x$ with an uncertainty $\pm e$, what would be the uncertainty in $\sin x$, $\pm\sin e$? ...
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22 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
45 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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65 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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1answer
23 views

What is the error on a counting variable?

I don't know if a variable that acts as a counter has an associated error. I don't see it as a measured quantity so I think that it has no error. The problem is this: you have an image of a star and ...
2
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1answer
137 views

Margin of error for quotient of two measurements

I need to find the total margin of error for calculating velocity, while I have margins of error for time and distance. Actually the margins are the same (as both measurements were based on GPS - but ...
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1answer
48 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 ...