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Questions tagged [error-propagation]

Methods for calculating errors of a function whose arguments have individual errors.

176 questions
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Using full covariance matrix of a linear fit reduces the errors?

I am currently studying linear fitting and error propagation. The model to fit is this: $$B ( N , Z ) = a _ { v } A - a _ { s } A ^ { 2 / 3 } - a _ { c } \frac { Z ( Z - 1 ) } { A ^ { 1 / 3 } } - a ...
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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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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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24 views

Error related $\frac{1}{u}$

I'm trying to calculate a value using linear regression with real data.The relation that will be used for this is: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$. The data I have is let's say $u \pm \delta ...
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21 views

Ratio error propagation for dependent, paired variables

I've been struggling for some days with a statistical issue that is beyond my knowledge. Context: I'm studying the volume of cells, as well as their nucleus volume. These cells are categorized in 3 ...
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1answer
15 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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49 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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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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17 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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87 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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34 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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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
67 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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307 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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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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19 views

Is a propagation of errors necessary in this scenario?

Please forgive my poor formatting, I'm still learning how to use this website. I've been doing some experimental design work and I'd appreciate some feedback. A central composite design was used to ...
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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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8 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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160 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
74 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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54 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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284 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
389 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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13 views

Uncertainty propagation with unsuccessful curve fits

I have a set of measurement results and their uncertainties that I need to fit to an implicit nonlinear function of four parameters. If the uncertainties are large enough, this works like a charm. If ...
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1answer
50 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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21 views

How does errors in yi affects the error of the slope in linear regression?

I have x and y values. The y values are calculated somewhere else and are reported as y ± error. I want to do a linear fitting of "x and y± error". How would the errors of y affect the error of the ...
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25 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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26 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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68 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
211 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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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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89 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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113 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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20 views

Determining statistical significance between processed data sets

I am a scientist looking to determine statistical significance between some experimental data sets I've collected. Unfortunately, I'm quite at a loss as to how to ...
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69 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 ...
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49 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
52 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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79 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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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 ...
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1answer
77 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
50 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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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
65 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 ...
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34 views

Using z ~ y regression based on y ~ x regression: how to propagate the errors of both regressions?

Somebody asked this similar question about 7 years ago and it received no response (Error propagation in consecutive regressions) Suppose I run a regression $$y = a + b x + N(0,\sigma_1)$$ that I can ...
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1answer
376 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
116 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
675 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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63 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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