Questions tagged [error-propagation]
Methods for calculating errors of a function whose arguments have individual errors.
321
questions
1
vote
0
answers
119
views
Uncertainty propagation and categorical data
Suppose that you have a model in which you want to perform uncertainty propagation. For example, consider a model of temperature in an area of the world. To simplify, in this model, Temperature will ...
- 11
0
votes
0
answers
3k
views
Ratio of standard deviations
I have paired data.
I do not have the individual data points - solely the means and standard deviations at measurement 1 (m1, sd1), at measurement 2 (m2, sd2), and also the correlation coefficient ...
- 253
2
votes
0
answers
2k
views
Quantifying uncertainty of regression models
I have built various different types of regression model (linear model, non-linear model, generalized linear model), and wish to determine the error/uncertainty of each one in order to compare them.
...
- 487
2
votes
0
answers
364
views
Propagating errors through interpolation and maximisation
I have a spectrum of some counts against wavelength, where both the counts and wavelength have a known error. I then have applied a Hermite interpolation to the spectrum in Mathematica. From what I ...
- 41
0
votes
0
answers
657
views
Propagating asymmetric and large errors in a ratio
I'm currently trying to propagate the errors of two values:
$A=143^{+28.6}_{-26.6}$ , $B=19^{+10.9}_{-8.7}$ $\rightarrow$ $B/A = 0.133^{+?}_{-?}$
Both values A and B (#counts) are derived from a ...
- 101
1
vote
1
answer
173
views
Calculating variance of $c=a/b$ based on $\sigma_a$ and $\sigma_b$ (error propagation)
My problem concerns the calculation of variances in 2 different ways (the variances calculated in the 2 different ways do not seem to match)...
I have the following data:
For variable $A$: $\;\;\;...
- 175
4
votes
2
answers
3k
views
How do I calculate the variance-covariance matrix for a set of 2-D data points with errors: (x, y, dy)
I am doing a weighted linear least squares fit to N measured values of the form $(x, y, dy)$, where $x$ is the independent variable, $y$ is the independent variable, and $dy$ is the error estimates ...
- 391
0
votes
0
answers
46
views
Showing that an increase in uncertainty is significant
I have a linear model $y = ax+b$ and I estimate the coefficients $a$ and $b$ in the ordinary way.
I have found out that all of my values of $x$ were systematically overestimated, and also that they ...
- 3,112
2
votes
0
answers
80
views
Uncertainty propagation
I am having an issue solving the following problem. I am propagating the uncertainty of some input parameters through a mathematical model represented by $u$ to determine the uncertainty on an output ...
- 83
3
votes
1
answer
201
views
Accounting for uncertainty in a fit coefficient
So given some empirical data of $I_T$ vs $r$ I'd like to fit that to some model given by
$$
I_T=\frac{I_0}{1+F \sin\bigg(\frac{2\pi d}{\lambda}\frac{f}{f^2+r^2}\bigg)}
$$I am trying to analyze data ...
- 131
1
vote
0
answers
17
views
Exact Corrections to Measured Data in a Paper?
http://fy.chalmers.se/~f7xiz/TIF080/pendulum.pdf
I am really confused by this paper. They make corrections to the value of $g$ from theoretical corrections, but they plug in measured values with ...
- 133
1
vote
0
answers
333
views
Parameter uncertainty in Least Squares fit to Vector Valued Function
Suppose I have to fit a vector field $\vec{y}_i$ with a vector valued function $\vec{f}_i = \vec{f}(\vec{x}_i; \vec{p})$, so both $\vec{y}_i, \vec{f}_i \in \mathbb{R}^m$, where $\vec{x}_i \in \mathbb{...
- 121
4
votes
1
answer
1k
views
Calculating the uncertainty on a ratio result in A/B test
If I am running an A/B test in which I have two randomly assigned groups of users and I am calculating a conversion on some action, how do I then calculate the uncertainty on the result?
For example, ...
- 937
1
vote
1
answer
67
views
Error Propagation and Error Partition
Given a a general form of a model $F$ ( which could be an explicit formula or set of formulas) with its input $x$ and output $y$.
Suppose that the input $x$ has an error $\delta x$, so that given ...
- 867
10
votes
1
answer
11k
views
Linear model where the data has uncertainty, using R
Let's say I have data that has some uncertainty. For example:
X Y
1 10±4
2 50±3
3 80±7
4 105±1
5 120±9
The nature of the uncertainty could be repeat ...
- 599
2
votes
0
answers
72
views
Type B uncertainties and statistical analysis
In the Guide to Uncertainty in Measurement (GUM), two classes of methods to evaluate uncertainties are distinguished : a type A evaluation is a statistical method, applicable when a set of ...
- 121
1
vote
0
answers
267
views
Uncertainties on fitted parameters in least squares circle fit
To fit a given a set of data points (x,y) to a circle, one can use a least squares fit and obtain values for the center of the circle (xc, yc) and the circle's radius (R).
However, each of the data ...
- 21
1
vote
0
answers
3k
views
Line of best fit for data with error in x and y
I have a two dimensional dataset which comes from prior statistical analysis. Each point $(x_n,y_n)$ in the dataset has an error estimate $\sigma_{x,n}, \sigma_{y,n}$ for both coordinates. The $x_n$ ...
- 2,649
2
votes
0
answers
110
views
Propagation of uncertainty through a correlation with its own uncertainty
So I'm trying to do propagation of uncertainty for the first time (read: I'm a noob at this), and it's proving to be a challenge. I'm trying to estimate the uncertainty in the friction factor of the ...
- 21
0
votes
0
answers
26
views
Find error on the inputs
Suppose that we have a model with an input and an output. The model is exact (no structural uncertainty). However there is an error in the output ( the error is detected from already given exact ...
- 867
6
votes
2
answers
2k
views
Uncertainty in a fractional count
What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
- 211
3
votes
1
answer
2k
views
Propagate errors in measured points to Simpson's numerical integral
I have a set of measured/observed $y(x)$ points, each with an assigned standard deviation:
$$y: \{y_0\pm\sigma_{y_0}, y_2\pm\sigma_{y_2}, ..., y_N\pm\sigma_{y_N}\}$$
I use scipy's implementation of ...
- 4,292
1
vote
0
answers
742
views
error propagation on the median
Suppose to have a set of exact data $x_i, i=1,\dots,N$ and to calculate its median value $m$. Then, a sound way to estimate the error $\delta m$ on $m$ would be bootstrapping. (I think...)
But what ...
- 285
4
votes
1
answer
14k
views
Calculating uncertainties for histogram bins of experimental data with known measurement errors
I have a set of experimental data (with each data-point having its own measured uncertainty), and I wish to produce a histogram of it. The x values of the edges of each bin are already defined. The ...
- 43
5
votes
0
answers
181
views
How to mitigate the hierarchical error propagation in tree-structured classification
Suppose we have a multi-class classification problem, where the number of classes $K \geq 3$
We use a tree structure of multiple SVMs to divide and conquer the problem, with one example in the figure ...
- 51
0
votes
1
answer
2k
views
Estimate error of predicted value obtained by linear regression model
I have measured 2 parameters, r and p. Each parameter was measured in three technical replicates (n=3) per sample. r is measured directly. p is measured indirectly; the data obtained is output ...
- 1
3
votes
0
answers
646
views
Error in Linear Regression Parameters: Using mean measurement vs. all measurements
I have a set of measurements y taken at 17 different values of x, with 50 repeated measurements at each value of x. They follow a simple linear relationship y = mx + c, and I am fitting the parameters ...
- 31
4
votes
1
answer
494
views
Combining measurements with known uncertainties
I have $N$ rulers that each have a different but known level of accuracy, e.g. one's a meterstick, one's a yard stick, etc.
I measure the length of my table using each ruler.
How do I combine ...
- 3,112
0
votes
0
answers
1k
views
Error equation for distance between points in spherical coordinates
(Question brought over from here, after asking here)
Consider two points with spherical coordinates: $a=(r_1,\theta_1,\phi_1)$ and $b=(r_2,\theta_2,\phi_2)$. The cartesian coordinates of the points ...
- 4,292
0
votes
0
answers
1k
views
uncertainties from Monte Carlo simulation and error propagation are different
Inspired by this post Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?, I try to check it myself using a simple function f=A/B, where A is 10 with uncertainty 1 and B ...
- 1,272
4
votes
2
answers
2k
views
Propagation of uncertainty through a linear system of equations, Ax=b, where A and b are correlated
I have a linear system of equations in the form Ax = b. The elements of A and b were experimentally determined and as such have some uncertainty. Within each row, A and b are correlated. Between rows, ...
- 96
1
vote
0
answers
60
views
Confidence interval for the median - continued
I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$.
The $x_i$ values are the result of a maximum likelyhood estimation and their ...
- 285
8
votes
1
answer
2k
views
Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?
If I have a deterministic, analytic model, $y=f(x)$, I can analytically calculate the uncertainty in $y$ from a known uncertainty in $x$, $\sigma$. Or I can do a Monte Carlo integration: sample from ...
- 5,453
0
votes
1
answer
595
views
Generalised linear models error distribution (continuous response)
I'm a bit confused about what error distribution I should use for the generalised linear models that I am running. My response variable is litter decay rate (k) (continuous, which runs from -1.5 to +1....
- 3
3
votes
0
answers
187
views
Propagating uncertainties using random forest out-of-bag accuracy estimates
Let's say I train a random forest on some data and get an out-of-bag accuracy estimate of 90%. I then predict a quantity using this trained forest. What should be the uncertainty I give to that ...
- 3,112
6
votes
3
answers
4k
views
How to combine two measurements of the same quantity with different confidences in order to obtain a single value and confidence
Back in the lab at university, we were taught to measure the quantity of interest some number of times (call this N), and then calculate the standard error. The underlying assumption here is that you ...
- 2,422
1
vote
2
answers
4k
views
Adding Up Margins of Error
I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same ...
- 123
1
vote
0
answers
230
views
Monte Carlo error propagation
Consider a set $X$ of $N$ iid random variables, each one with its own standard deviation:
$$X: \{x_1\pm\sigma_1, x_2\pm\sigma_2, ..., x_N\pm\sigma_N\}$$
Say I have a "black box" numerical function ...
- 4,292
2
votes
2
answers
13k
views
Error propagation in a linear model
I am currently interested in learning more on error propagation. At the moment I am trying to find out how to calculate the uncertainty of a value that is obtained from a linear model. For the linear ...
- 33
3
votes
0
answers
110
views
Do Monte Carlo perturbations capture all the uncertainty in prediction?
I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$.
...
- 3,112
10
votes
2
answers
2k
views
How to propagate uncertainty into the prediction of a neural network?
I have inputs $x_1\ldots x_n$ that have known $1\sigma$ uncertainties $\epsilon_1 \ldots \epsilon_n$. I am using them to predict outputs $y_1 \ldots y_m$ on a trained neural network. How can I obtain ...
- 3,112
3
votes
1
answer
125
views
Propagate uncertainty of a parameter through a function
Suppose I have a probability distribution (in fact I've got a nice case where that distribution is Gaussian) on a parameter value. e.g. the parameter $x$ has $\mu = 3$ and $\sigma^2 = 1$.
Now suppose ...
- 33
12
votes
3
answers
32k
views
Variance of an average of random variables
This seems like it should be a pretty common problem. I have four estimates of fishing effort, each with its own variance. For subsequent calculations, I want the mean of the four estimates, and a ...
- 155
1
vote
1
answer
72
views
Are the parameters of Non-linear regression independent of each other?
I'm propagating error in the parameters determined by the following growth function...
$$
\hat{y} = ae^\frac{t}{b} + (1- a)e^\frac{t}{c}
$$
Say I have another model that uses the parameters {a,b,c} ...
- 13
4
votes
1
answer
8k
views
Backpropagation with Cross-entropy Cost Function
I'm using the cross-entropy cost function for backpropagation in a neutral network as it is discussed in neuralnetworksanddeeplearning.com. I got help on the cost function here:
Cross-entropy cost ...
- 527
11
votes
2
answers
36k
views
Cross-entropy cost function in neural network
I'm looking at the cross-entropy cost function found in this tutorial:
$$C = -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$
What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ ...
- 527
1
vote
1
answer
2k
views
Error propagation and relative error
Say I have measured the value
A = 50 +- 2
and from this I am calculating the value:
B(A) = A^2
From what I understand I calculate the new error using error propagation to be
delta_B = dB/...
- 153
2
votes
1
answer
126
views
How to consider propagated measurement errors and "statistical errors"
I come from an Engineering background, and I am familiar with some basics of error treatment. However, discussing with a friend over some data he had to analyze, we couldn't quite figure out what to ...
- 21
1
vote
0
answers
2k
views
What is the correct way to combine data points with error?
If I have a 2-D data, say $y = f(x)$, with error in the dependent variable, $\delta y$ in this case, and I want to transform this data set to a coarser independent variable grid, $x$, what is the ...
- 391
3
votes
0
answers
2k
views
Adding numbers with asymmetric uncertainties
I need to add a series of numbers with asymmetric standard deviations, such as
$$5_{-2}^{+1} \,+ \,3_{-3}^{+1}.$$
Although I know it's common to add the upper errors ($\sigma_{\scriptsize{+}}$) and ...
- 131