Questions tagged [error-propagation]
Methods for calculating errors of a function whose arguments have individual errors.
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What is the error on the weighted mean?
I am combining bins in the histogram. I have some code that uses this formula to calculate the error on the weighted mean:
$$\sigma = \frac{\sqrt{\sum \frac{w_{i}(w_{i}\sigma_{i}^{2}+x_{i}^{2})}{\sum ...
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Relating covariances for (θ, Χ) and (cos(θ), Χ)
From basic error propagation rules, we have σ(cos(θ)) = |sin(θ)| σ(θ).
Question: does something similar hold for the covariance cov(cos(θ),X) and cov(θ,Χ)?
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Uncertainty propagation for quadratic interpolation
I have timeseries data $(t_i, y_i)$ with uncertainties $\Delta y$. I need to interpolate this data to match the timestamps with the timestamps of another dataset.
Theory
To propagate the uncertainties,...
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Neural networks with uncertainties in training data
I have used Flax to train a neural network to fit a model to some data. All of the data points have a known uncertainty, as in each row has both a value and an uncertainty. (To be more explicit: the ...
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Propagation of uncertainties for high signal-to-noise ratio measurements
I am writing mass spectrometry data reduction software which calculates 4He volumes, and I have some questions about the propagation of uncertainties.
The system in question measures helium volumes by ...
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How to determine the confidence intervals for the principal axes of a second-rank tensor?
The question in short: How does one estimate the confidence intervals for the principal axes of a second-rank symmetric tensor when the measurement errors are themselves a function of the values of ...
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How can I provide meaningful commentary about the uncertainty associated with a population estimate drawn form individual ML predictions?
Context: Suppose a team develops a prediction model that predicts the presence of a condition for a given individual. This model is trained and externally validated before being picked up by a ...
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Error propagation: How to sum errors over 2D grid?
I have a dataset with worldwide mass change data and their uncertainty from glaciers. Both have dimensions 720,360,45 with the first two dimensions 'i,j' (lat,lon) coordinates and the third dimension '...
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Interpolation of errors from model predictions over time-series
I have a regression model:
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Converting the unit for mean and standard deviation
I have a problem and it's been days and I couldn't find a solution
Simply what I want to do for the purpose of a research data, I have the mean and standard deviation of some measurements in diameter ...
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Standard Deviation and Standard Mean Error of measurement with uncertainties
It is well known that, given a set of $n$ values $Y_1, \cdots, Y_n$, its Sample Standard Deviation is $\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^n (X_i - \bar{X})}$ and its Standard Mean Error is $\...
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When error propagation is necessary in modelling?
This is a somewhat philosophical question. When executing classical statistical modeling, such as regression, LM, GLM, mixed modeling, etc., there is often no mention of propagating the error of the ...
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Confidence and prediciton intervals for power law fit
I would like to determine confidence intervals and prediction intervals for a noisy dataset that follows a power law distribution.
I have a dataset that (to my eye) follows power law behavior in the ...
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Doesn't aggregating time series sometimes throw away quantifiable uncertainty?
Introduction
From time-to-time I hear a claim that it is better to forecast on aggregated data because it is more "stable" or has less uncertainty.
Here is an example, although I know I have ...
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How would one describe such irregular data?
The situation is as follows (physics based): I have an array (7) of pixel sensors (imagine phone cameras) and a ton (millions) of particles crossing them (very large N). Each particle crossing a ...
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