Questions tagged [error-propagation]
Methods for calculating errors of a function whose arguments have individual errors.
323 questions
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SE of a product
How can I compute the standard error from this formula below if each variable $X_i$ is the correlation coefficient of samples with a different sample size.
$$\begin{align}
\operatorname{var}(X_1\cdots ...
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What is the generalized univariate change-of-variables formula? [duplicate]
I have a normally-distributed random variable $I$ with a few sample points and a given standard deviation $\sigma$.
I need to transform the random variable, its samples and its standard deviation ...
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Error propagation in variance calculation
Let's assume that I have $n$ measurements $\mathbf{x} = (x_1, ..., x_n)$ of a given quantity $X$, e.g. regression coefficients. Each $x_i$ has a corresponding standard error $SE_i$. I'd like to ...
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When do I use standard deviation of a variable vs. error propagation of that variable when determining uncertainty?
Let's say I have 2 quantities to measure, $x$ and $y$. They do not have uncertainty but I can make repeated measurements to determine their uncertainty via standard deviation. Then say I want to find $...
Jonah George
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Relative vs. absolute error bars in log-scaled plots
There's conflicting info from seemingly knowledgeable sources about the correct way to show error bars on a log-scaled plot.
$log_{10}(x \pm \Delta x)$ shows the absolute error. On the one hand, it's ...
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How do I calculate the error propagation for an estimated parameter?
Assume that I have a resistor with an unknown resistance R. I measure the current trough it, I, and the voltage across it, U.
I can then estimate R:
$$
\hat{R} = \frac{U}{I}
$$
Let us assume I get the ...
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What is the error on the weighted mean?
I am combining bins in the histogram. I have some code that uses this formula to calculate the error on the weighted mean:
$$\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 $\sigma = \sqrt{\dfrac{1}{n-1}\sum\limits_{i=1}^n (X_i - \bar{X})}$ 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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Error propagation. Simpler average errors
I am designing a lab practicum to study error propagation. Let's suppose I will measure $x \pm\varepsilon_x$ and $y \pm \varepsilon_y$, where $\varepsilon_x = \varepsilon_y = \varepsilon$ for ...
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What is the standard error of a binomial process with a false-positive rate
I have a question that must be common, but after searching, I can't find an explanation. Suppose we wish to estimate the percentage of people, p, who have a disease. We test n people. The test has ...
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Calculate mean and standard deviation of the ratio of two dependent variables
I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
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Estimating the error bounds for a derivative chart of data
I have collected position (S) versus time (t) data. A typical result is shown in the following chart:
As can be seen all three regression models provide excellent fits to the mean values of the data ...
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Uncertainty in values predicted using a linear regression
I am quite new to statistical analysis, so this question might seem a bit obvious. My problem is the following. I have performed a simple linear regression between two sets of values without ...
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Propagation of error from statistical error
We have done the determination of protein abundance in two fractions (M and P) in one condition (SP).
We've done three biological replicas.
The data obtained are:
\begin{align*}
&\text{SP (...
Paula Portela
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Error propagation for arbitrary function with a very large number of variables
let's say I have some function, $f(\vec{x})$, whhere the input is a vector of very large size $\vec{x}=[x_1,x_2,x_3,...x_n]$. n is tens of millions, but let's say for now it's just very large. I can ...
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Prediction Interval when independent variable has variance
Given an existing regression curve, how do I properly account for the known variance I have in some new value of X? If I had an observation $x_{new} = 700$ with a variance $\sigma_x^2 = 150$ then how ...
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Calculate the average of absolute values of a measurement with a measurement error
I have a few parameters; each is measured imprecisely with a known but unique random
measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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Very Basic Question - Propagation of Error and Fold Changes in Medicine
Say you have measured three conditions (x, y, and z) together and at three separate times (three replicates). These raw values are normally distributed and in a linear space.
You use those three ...
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How can I combine model parameter uncertainty and input uncertainty?
Suppose I have a finite data sample $\mathbf{S} = \{ (\mathbf{x}^{(1)}, \mathbf{y}^{(1)}), \dots, (\mathbf{x}^{(N)}, \mathbf{y}^{(N)}) \}$ from an unknown data-generating function of the form
$$ \...
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Can be the output distribution non-normal using the moment method?
I want to study the uncertainty propagation through a nonlinear function $Y = f(X)$. I am assuming that $X$ is normally distributed and I am using the moment method approximating $f(X)$ by its first (...
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Propagation of uncertainty in a derivative of a function [duplicate]
I've performed an ordinary least squares on a data set with one variable. For simplicity, let's say I've fitted a polynomial function
$$f(x)=a+bx+cx^2+dx^3.$$
I obtain the best fit and the standard ...
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Relative error on a log-log plot
Since absolute error plotted on a log-log plot will result in asymmetric error bars, my understanding is that this would give a misleading view of the precision of a measurement. I can plot instead ...
user142054
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Estimating uncertainties in parameters from minimization of an expression
I was curious if they are anything in the literature about estimating or propagating uncertainties when the desired result is from the minimization of an expression. I have several books on ...
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How to propagate errors from two sources
Suppose I performed 10 measurements, and have the dataset:
...
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Fitting data taking into account for the spread in data, which are zero for some data points
I'm trying to use scipy to fit a $\tanh$ function to some data. The data is of the form $(x_i, y_i)$ for $i=1,\cdots,N$, where $0\leq y_i \leq 1$. I choose $x_i$ to be linearly spaced, such that $x_0=...
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Include confidence intervals of samples in nlme model
I have a continuous response variable (leaf length), which has been repeatedly measured in 45 experimental plots over several growing seasons. My goal is to properly estimate at which day of the year (...
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Effect of Simulation Error on the Monte Carlo Estimator
Given a random variable $X$ with known pdf $f$ and some computer simulation model $g(x): \mathcal
R \rightarrow \mathcal R$, mapping samples $x \sim f$ to a scalar metric $g$, we can estimate the ...
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how to propagate uncertainty in probability values
If you are modeling probability of events (eg classic dice rolls or coin tosses) but want to represent probabilities as normal distributions, how do you propagate the uncertainty from individual ...
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Prediction error after mean-centring/transforming/etc. input data?
Suppose that I have a linear model of $p$ parameters ($f(p,x)$) that I want to fit to my dataset using least squares. According to Wolberg (2006), the prediction error in $\hat{y}$ can be calculated ...
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Measure of goodness of polynomial fit at specific points or weighted analysis?
I have some astrophysics data of "particle density vs orbital position" of a moon that emits a lot of particles. My research deals with the intensity of the scattered light which is ...
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Incorporating denominator uncertainty into a proportion
I am calculating an incidence risk (r): number of cases of a disease in a population over one year (c) divided by the total mid-year population (N).
$$
r = \frac{c}{N}
$$
Let's assume that c is a ...
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P-value testing on data with known errors
I have two cohorts, Long COVID vs control. They have been using a fitness tracking device for two months. I want to see if there's a significant difference in Sleep stages, Resting HR, and step counts....
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How would one find the uncertainty in a mean if the data points themselves have zero-order uncertainty?
Sorry if this question is this community's equivalent of asking a chef how to boil water, but if you had a data set that consists of:
[A±a, B±b, C±c, ..., N±n], where each value has a corresponding ...
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Accounting for measurement error in the one-way ANOVA test and Fisher's LSD
I am working with 5 groups of measurements, all having a measuring uncertainty of 0.5 mm - I used the one-way ANOVA test to reject the null hypothesis and Fisher's Least Significant Difference to ...
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Calculating uncertainty of predictions - standard error or error calculus?
I'm looking to create a calibration function for a lab instrument I have:
$y = A + Bx$
Where $y$ is the "true" output and $x$ is the initial reading. I have a dataset of ~100 readings that I ...
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Does it make sense to take a weighted average over cross validation results?
I am using P-splines to estimate an unknown function $f(x)=y$ that I am fitting to data $x,y$. I am using cross validation to estimate the roughness parameter.
It is important to me to not only ...
- 3,132
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Standard error, standard deviation and error propagation
I measured a quantity 100 times to get 100 measurements denoted as $x_1$, $x_2$, ..., $x_{100}$, with uncertainties as $e_1$, $e_2$, ..., $e_{100}$. Now if I want to report the average of these 100 ...
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