# Tagged Questions

For questions on propagation of errors.

553 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 ...
99 views

### Avoiding loss of numerical accuracy

I need to to evaluate the function $f(x) = {1 - (1-A)^x \over A}$, where $0 < A \leq 1$ and $0 \leq x \leq 1$. A straightforward C implementation of $f(x)$ with floating-point arithmetic works ...
3k 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 ...
204 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 ...
962 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 ...
53 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 ...
132 views

### Absolute and Relative Error of $x^y$

Suppose that we have two measured values $x$ and $y$ with maximum absolute errors of $e_x$ and $e_y$. Is there a formula to find a good upper bound for absolute and relative error of $x^y$?
67 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 ...
202 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 ...
88 views

### Confused about the explicit formula for $\psi_0(x)$

In the explicit formula for $\psi_0(x)$ used in the PNT proof : $$\psi_0(x) = x - \sum_{\rho} \frac{x^{\rho}}{\rho} - \frac{\zeta'(0)}{\zeta(0)} - \frac{1}{2} \log (1-x^{-2})$$ In particular the ...
53 views

### Looking analytically if one formula is better than another one

I'm studying errors in functions on numerical methods. On my notes, I've written the Heron's Formula: Let $a\geq b\geq c$:$$A=\sqrt{p(p-a)(p-b)(p-c)}\ \ ,$$ where $$p=\frac{a+b+c}{2}.$$ This formula ...
66 views

33 views

### Are the “weights” inside a neural network actually “terms” for a polynomial?

This just hit me today. I am not too experienced with math or neural networks, but I am trying to find out about them in my own way so I can some day understand them well. So I was thinking about how ...
138 views

216 views

### Angle between two vectors with noisy data?

Given two vectors V1=(x1,y1,z1) and V2=(x2,y2,z2) I can calculate the angle between the two vectors using the dot product of the two vectors and their magnitudes. This approach, however, is only ...
225 views

### Derivation of formula for estimating error in bulk-volume

In my textbook, a formula for estimating error in bulk-volume measurements is derived, but I don't quite follow one step in the derivation. The book writes the following: The bulk volume of a porous-...
I am getting confused about a super basic issue. I have two quantities: $6\pm4$ and $4\pm3$ . So let's say $x = 6$, $\Delta x = 4$, $y = 4$, $\Delta y = 3$ Now I want to calculate the uncertainty ...