Questions tagged [error-propagation]
Methods for calculating errors of a function whose arguments have individual errors.
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 $A$: $\;\;\;...
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2
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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{...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $x_n$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $y$.
...
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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 ...
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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 ...
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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 ...
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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} ...
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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 ...
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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 $a$ ...
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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/...
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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 ...
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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 ...
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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 ...