Questions tagged [error-propagation]
Methods for calculating errors of a function whose arguments have individual errors.
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29 views
Calculating an overall standard error/confidence interval across multiple datasets
I am using five different datasets (with 250,000+ samples in each) to calculate an overall average across them. I also would like to calculate an overall standard error/confidence interval for them.
...
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30 views
Error propagation in Gaussian processes
I am trying to predict a time-series measurements, $x_{t+1},x_{t+2},...$ using a Gaussian process model, where the kernel is a Gaussian kernel with small noise-level $\sigma_w^2$, i.e. $k_{ij}=e^{-\...
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1answer
18 views
Propagation of asymmetric uncertainties
I have two (fully independent) measurements of the same quantity X.
Each of them reports a measurement $X_{\sigma_L}^{\sigma_R}$ where $\sigma_L$ and $\sigma_R$ are the left and right uncertainties (...
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11 views
Include standard error of values of an independent variable?
Values for one of my independent variables include reported standard errors. Is there some way to include these standard errors (of the values of the IV, not of its coefficient) in a regression model -...
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1answer
26 views
Propagation of uncertainty when summation symbol is involved
I am unsure how to estimate the propagation of uncertainty when there is a summation symbol involved.
I have the formula (its used to calculate the sauter mean diameter but I will give a simpler ...
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1answer
36 views
Standard error of mean vs error propagation
I'm confused on how to correctly calculate the final uncertainty from averaging measurements that each have their own internal errors.
Say I have 3 voltage measurements: (1.232 ± 0.001) V, (1.197 ± 0....
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60 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 ...
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1answer
14 views
Error propagation in dividing the averages of two data sets
Let's say I have two data sets each containing 1000 points. I want to get the respective averages of both data sets, then divide the resulting averages. What is the best way to propagate the error (e....
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19 views
Propagation of error from y into x
I have a question about error propagation. The figure below shows HDD as a function of temperature.
I have determined a minimum in HDD (approximately 1 at approximately 11 degrees) with corresponding ...
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34 views
Fitting model with error on independent variable
This is the second part of a question started here. However, as this touches a different problem inside the same overall issue I decided do separate it into two questions.
I've made a series of ...
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117 views
Converting standard deviation of percent change to absolute change
I have the following data:
However, I wish to know the standard deviation of the absolute change rather than the percentage change.
To clarify, for Cloz: absolute change = 0.14*53 = 7.42, and we are ...
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35 views
Covariance in an error propagation leading to negative variance
Does it ever make sense that, propagating the error from a set of data, the covariance term being very negative makes the variance go to a negative value (which by itself makes no sense)?
Context:
...
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101 views
Calculating the covariance between 1-D arrays for incorporation into propagation of uncertainty
I have four 1-D arrays of dependent variables. They contain hundreds of data points but I have cropped them to 20 in this example. Each point represents a grid cell on a map.
...
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1answer
91 views
Confused about h-step ahead forecasts
I have 12 months of in-sample data and 12 months of out-of-sample data. I'm trying to calculate the scaled error for an h-step ahead forecast where h=1, 6 and 12. Do I just calculate the error at ...
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0answers
464 views
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,...
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21 views
Error propagation through an integral with normal distribution weighting
I have the following equation:
$I(a) = \int_{-\infty}^{\infty} \frac{1}{\sqrt{2\pi \sigma^2}}e^{-(x/\sigma)^2} rect(a) dx = \int_{-a}^{a}\frac{1}{\sqrt{2\pi \sigma^2}}e^{-(x/\sigma)^2} dx = \frac{1}{\...
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28 views
Error Propagation in R in ANOVA
I have a set of categorical x variables mapped to numerical y values. The y values have a known error (from measurement by an instrument) that I want to take into account when running an ANOVA. I am ...
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11 views
Calculation of the acceleration correction for BCa bootstraps for data with known errors
I have paired measures for a set of data, and these measures have associated uncertainties. I'm attempting to correlate them using Kendall's tau-b (as we have reason to believe that while they are ...
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188 views
Error propagation in linear regression
I have a question to error propagation with linear regression. I've thought about this problem for a while now and just can't find how it's done.
So basically I have performed around 60 measurements ...
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1answer
122 views
How do I propagate error for a Poisson-binomial distribution (sum of probability estimates with standard deviations)
My question is about quantifying the uncertainty associated with a sum of several probabilities, in a case where the probabilities are unequal and are themselves estimates with associated uncertainty (...
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56 views
Uncertainty of an integral estimate
I am making the following estimate:
\begin{equation}
\langle f \rangle \simeq \int_0^1 \left[ f(x) \cdot K(x) \right] \; \text{d}x
\end{equation}
where
$f$ is an unknown function, possibly $f(...
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1answer
464 views
Propagation of error in log ratios
I have experimental "before" and "after" measurements that I need to compare. The standard way in the field is to look at the log ratio, $y = \log_2(\frac{a}{b})$, so no change is $0$. I'm trying to ...
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1answer
455 views
calculate standard deviation for cumulative sum [closed]
I have data which is x and y as shown below. x and y have standard deviation x_sd and y_sd.
I have calculated cumulative sum for x, and x*y as shown below (x_cumsum & xy).
Now I need to calculate ...
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1answer
57 views
Error propagation in combined linear models
I have a set of observed values ($y_{1Obs}$) and 3 predictive variables (n = 27). I use multiple linear regression to create a linear model:
$Z_1=\alpha_0 + \alpha_1 W_1 + \alpha_2 X_1 + \alpha_3 Y_1$...
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26 views
Exploiting the joint density when averaging measurements
I have two measurements of a quantity from two different sensors, each with their own variance based on the sensors' specifications, etc. From collecting a lot of training data, I have access to the ...
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0answers
28 views
group average taking into account individual uncertainties
I am interested in the mean and variance over n random variables $x$ where each $x_{i}$ is independently distributed with an unique mean and standard deviation, $x_{i} ~ \sim \mathcal{N}(\mu_{i}, \...
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74 views
Propagation of Absolute Error in Weighted Linear Regression
This is probably relatively trivial, but I am having a difficult time searching for what I want.
I have a set of measurements with a well-defined variance, and I'm performing a weighted least squares ...
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1answer
225 views
Is standard error propagation appropriate in this situation, and if so how, and why?
I have a real-world problem which has left me puzzled in terms of how to approach it with any degree of rigour. I'm not a statistician,, and although I can understand it enough to produce a vague ...
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0answers
17 views
Error of weigted average of elements with errors
I have a set of data with errorbars ($x_i, \sigma_i$), and I need to compute a weigted average and the error. I used the formulas from https://ned.ipac.caltech.edu/level5/Leo/Stats4_5.html
For the ...
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0answers
98 views
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, ...
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votes
2answers
127 views
Multiplying means and calculating variance
I have multiplied together two means and now want to calculate the overall standard deviation. The two means and standard deviation are here: 13.7 +/- 12.7 (1SD) and 4.0 +/- 2.6 (1SD). So the answer ...
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0answers
70 views
So many ways to calculate the t-statistic - is this the 'super-formula' I need to yield all the different forms?
I've noticed that the formula for the t-statistic takes on a number of forms depending on the nature of the test being performed, i.e.,:
one sample
independent samples (equal variances)
independent ...
3
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0answers
54 views
Error bars for sum of Monte Carlo integrations
I want to calculate a quantity $I$ which is the sum of integrals $I_k$,
$$
I = \sum_k I_k\;,\quad I_k = \int_{\Omega} f_k(x)\,\textrm d x\;,
$$
Every integral $I_k$ is evaluated independently by a ...
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1answer
58 views
uncertainty in error propagation of normally distributed data?
I have two normally distributed random variables that add together to form a third normally distributed variable. The means in all cases are 0. Thus, the standard deviations of the first 2 variables ...
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0answers
90 views
Error propagation through a nonlinear model with error on constants as well as observations
I'm using the following equation to invert (non-linearly) for three parameters, L Vr and f.
$$T_r=\frac{L}{V_r} - \frac{(L\,\cos( \theta )\,\cos( \alpha - f))}{V} $$
I have observational errors on $...
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0answers
4k views
Extrapolating an error rate from a sample audit to a larger measurement
I have a report being generated from some transaction data (basically a list of items that should have been purchased) and I can also randomly sample the true transactions as they happen as an audit ...
2
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1answer
85 views
Error propagation through two consecutive regressions
I have one linear regression between a variable of interest (z) and measured values of another variable (y):
z = ay + b
and another regression between y and a proxy variable (x):
y = cx + d
I want ...
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1answer
51 views
Propagation of errors for a sum of fractions of random variables
Say I have a random variable $Z$ that is itself a function of two independent random variables $g(X,Y)$, where
$$Z = g(X,Y) = \frac{X}{Y}$$
I know that the propagation of uncertainty gives a good ...
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0answers
28 views
Find the error in an orientation angle for noisy points in $R^2$
Assume I have two points in $R^2$:
$P_{t=0} = (x_1, y_1)$ and
$P_{t=1} = (x_2, y_2)$
at $t=1$ I want to calculate the heading angle/orientation of the particle.
Both points have measurement noise ...
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1answer
19 views
Suspicion about the errorback propagation formula in PRML
From PRML:
Do variations in $a_j$ give rise to variations in $E$ only via $a_k$? True. Is $h'(a_j)$ the same across all $k$? I'm afraid not.
Let's write down what $\partial a_k/\partial a_j$ are....
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1answer
72 views
propagate uncertainty in mass balance
I have been using the Libre Office Solver tool (similar to Excel Solver) to mass balance some chemical systems. I know the chemical compositions of the various phases in the system and the chemical ...
2
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1answer
401 views
Unsure if my implementation of a Convolutional layer doesn't learn or it's the correct behaviour
So for the last week or so I've tried to implement a Feed Forward network with multiple types of layers (Fully Connected, MaxPool, Convolution), multiple types of non-linear functions (tanh, sigmoid, ...
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2answers
127 views
Combining uncertain measurements
I have a ball on a table located in position $x', y'$.
I am using many different rulers to measure the coordinates $x_i, y_i$ of the ball. I do this with $N$ different rulers, so $i = 1\ldots N$. ...
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1answer
959 views
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}...
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0answers
64 views
Sample number for confidence intervals of derived quantities
I have two related questions:
Assuming (as the extreme case) I measured a quantity (A) just twice, but I know that the values would "become" normally distributed if I measured the quantity repeatedly....
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0answers
45 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 ...
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0answers
732 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 ...
3
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0answers
665 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.
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0answers
105 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 ...
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285 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 ...
