All Questions
Tagged with uncertainty error-propagation
63 questions
3
votes
1
answer
33
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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 ...
- 75
0
votes
0
answers
14
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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
1
vote
2
answers
148
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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 ...
- 165
1
vote
0
answers
19
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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 ...
- 3,132
0
votes
0
answers
22
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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 ...
- 113
1
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0
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36
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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 '...
- 11
0
votes
0
answers
75
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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 ...
2
votes
0
answers
42
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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 ...
- 9,660
1
vote
1
answer
132
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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 ...
- 111
1
vote
0
answers
71
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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 ...
- 11
0
votes
0
answers
43
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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 ...
- 7,769
0
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0
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177
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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 ...
1
vote
0
answers
86
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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
$$ \...
- 113
2
votes
0
answers
20
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Can be the output distribution non-normal using the moment method?
I want to study the uncertainty propagation through a nonlinear function $Y = f(X)$. I am assuming that $X$ is normally distributed and I am using the moment method approximating $f(X)$ by its first (...
- 21
0
votes
1
answer
37
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Incorporating denominator uncertainty into a proportion
I am calculating an incidence risk (r): number of cases of a disease in a population over one year (c) divided by the total mid-year population (N).
$$
r = \frac{c}{N}
$$
Let's assume that c is a ...
- 137
10
votes
1
answer
527
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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 ...
- 203
0
votes
0
answers
57
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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 ...
- 71
1
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0
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71
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Distributions as Features in Machine Learning
The Problem
Let's assume I have a problem that seems perfect for supervised learning. However, some of the measurements I would like to use as features are not point estimates but are instead ...
- 153
0
votes
0
answers
807
views
What is the best way to fit data with multiple y-values per x-value and and get standard error at an extrapolated value?
I am running an experiment where I am collecting data for 3 x-values, say X = [x1, x2, x3] (each x > 0).
For each of the x ...
- 101
0
votes
0
answers
155
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What is the relationship between the residuals of an objective function and the uncertainties of the minimizer values?
Consider I have some optimization problem and an objective function $f(x, y, z)$.
$f$ is defined using the sum of squared residuals, i.e. for some function $g$, we have $f(x, y, z) = \sum[g(x, y, z) - ...
- 11
0
votes
1
answer
49
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Uncertainty when substracting average from the same data set
I have a data set with its own measurement uncertainties. Then I do averaging of the population and use standard error of the mean as the uncertainty for the average.
My question is, I need to ...
1
vote
0
answers
302
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Error propagation for cubic relationship
I have the cubic relationship between two variables, x and y, and I need to find the error in x.
y = ax^3 + bx^2 + cx + d
I have the values for the coefficients and their respective uncertainties. I ...
- 11
0
votes
1
answer
93
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Log and exponential uncertainty propogation
I am processing data on a radioactive decay experiment, and need to find the errors on some quantities that I can get from some fit parameters.
I would like to obtain:
$\sigma A$ from $A = e^{a}$, ...
- 149
1
vote
0
answers
139
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MLE like method for uncertain data
I have a rather basic question for which I could not find an answer for. I want to use a similar technique as Maximum Likelihood Estimator (MLE) or even MLE itself for data which has uncertainties for ...
- 51
1
vote
0
answers
79
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Bias of mean in toy Monte Carlo sampling of $A\times B$ for $A=a\pm\sigma_A$ and $B=b\pm\sigma_B$
I am trying to do some toy Monte Carlo sampling, to calculate the uncertainty of the product $A\times B$ of two random variables $A=a\pm\sigma_A$ and $B=b\pm\sigma_B$.
I also assume that these ...
- 111
2
votes
0
answers
228
views
Uncertainty calculation for mean of spatially gridded data
I have data on a spatial grid. For each cell of the grid there is a best estimate ($x_i$) and an uncertainty ($\sigma_i$) which is specific to that grid cell. I'd like to calculate the mean for the ...
- 121
0
votes
0
answers
20
views
Propagation of uncertainties when the parameter being calculated is not normally distributed, and neither are its components
I have an equation (linked here for simplicity as i can't format https://i.sstatic.net/l9bZS.jpg)
The parameters Tc, T0, Zb and Z0 are fixed.
hr is normally distributed
K is normally distributed in ...
- 1
0
votes
0
answers
157
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Method for removing data points that have high uncertainty
I have a set of data point $\{x_1, x_2, ... x_n\}$ each with some uncertainty $\{u(x_1), u(x_2), ... u(x_n)\}$. However, there exist a couple $u(x_i)$ that are 3 orders of magnitude higher than the ...
6
votes
1
answer
567
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Uncertainty propagation for the solution of an integral equation
I have a dataset and I use Maximum Likelihood Estimation to estimate the values of the parameters of a weibull distribution. The MLE theory provides with theoretical Confidence Intervals (asymptotical,...
- 1,817
1
vote
0
answers
134
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Gaussian Process Regression with independent variable uncertainty on datapoints
Imagine that I have a set of $N$ (training) datapoints $\left\{(x_n,y_n)\right\}_{n=1}^N$, with error bars/uncertainties on each datapoint along both the $x$- and $y$-directions, written as $\left\{(\...
1
vote
1
answer
138
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Propagating uncertainties of constants in division
I have two constants, $A$ and $B$, with associated uncertainties $\sigma_A$ and $\sigma_B$, from observational errors, for example. I need to perform calculations with these constants, by for example ...
- 539
3
votes
0
answers
260
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Uncertainty propagation in ODEs
I want to see the effect of parameter uncertainty in the Euler method for ODEs.
For a differential equation:
$dx/dt=f$
with initial condition $x(0)=xo$ and a function $f$ (that has uncertain ...
- 31
1
vote
0
answers
39
views
error propagation for derivatives
I have the following problem:
I have some data of a function f(x) with a set of 300 values of it associated to the same number of values of x including corresponding standard deviation σ(f) for each ...
5
votes
2
answers
2k
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What is the best way to report the results and uncertainty from a Monte Carlo simulation?
I am fitting data to a model that has ~30 input parameters, each with their own uncertainty levels, and which can interact with each other in the model. I therefore decided the best way to fit the ...
- 151
2
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0
answers
148
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How do I properly include systematic uncertainty of x and y values correctly into fitting parameters (y=ax+b)?
I am doing a simple experiment that involves measuring the resistance of a wire. To do this, we measure the voltage across a wire as we increase the the current going through it with two Fluke Digital ...
- 31
4
votes
1
answer
477
views
How to estimate the uncertainty in the zeros of a fitted function?
I have fitted points with a polynomial. I now have the coefficients and the covariance matrix.
For a given y (in this case y=0; that is, x is a root of the polynomial) what is the uncertainty of that ...
- 43
1
vote
0
answers
380
views
Propagating error when taking the derivative
I have a function that corresponds to a set of $(X,Y)$ coordinates with a Gaussian uncertainty ($\sigma_Y$) for each point. What I want to do is now compute the gradient of this function and the ...
- 599
1
vote
0
answers
776
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Handling negative variances on the derivative of Gaussian processes
The variance of the derivative of a Gaussian process, $f$, is given by (9.1):
$$ Var(\frac{\partial f}{\partial x}) =\frac {\partial ^2 k(x,x)}{\partial x^2},$$
where $k(·, ·)$ is both a positive-...
- 599
2
votes
0
answers
653
views
Cross-Correlation Propagation of Uncertainty
I would like to calculate the uncertainty of the cross-correlation of two functions (in two dimensions but even one-dimension is a great start). Experimentally, I have discrete values of f and g, and ...
- 205
6
votes
0
answers
4k
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Confidence Intervals with Propagation of Uncertainty
Lets say I'm trying to make a measurement of the area, $A$ of an object imaged in a large number of noisy gray-scale image, and I want to include uncertainty quantification to some confidence interval,...
- 161
1
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0
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240
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error propagation of oscillation removal of time series
I have a time series that that has the form:
$$
F(t) = C + \sum_i A_i\sin(2\pi f_i t +p_i)
$$
Where $C$ is a constant, $A_i,f_i,p_i$ are amplitude, frequency, and phase of the $i^{th}$ oscillation, ...
- 111
1
vote
1
answer
3k
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Uncertainty of a weighted mean of uncertain observations
I have measured $x_i$, $i=1\ldots N$ with independent uncertainties $\sigma_i$.
I have calculated the weighted mean $\bar x$ with
$\bar x = \dfrac{\sum_i \dfrac{1}{\sigma_i} x_i }{ \sum_i \dfrac{1}...
- 3,132
1
vote
0
answers
125
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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 ...
- 11
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
1
vote
1
answer
193
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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 $A$: $\;\;\;...
- 175
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 ...
- 3,132
2
votes
0
answers
82
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
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, ...
- 947
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
2
votes
0
answers
294
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 ...
- 31