Questions tagged [error-propagation]

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

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Least squares model selection criteria: standard error of point estimator vs variance of non-zero components in corresponding column of design matrix

I am performing ordinary least squares regression, and I would like some help with my model selection. One possible model is the following: The design matrix is denoted as $ \mathbf Z $ and the vector ...
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Weighted Least Squares vs Monte Carlo comparison

This is a copy of a question originally posted on stackoverflow I have an experimental dataset of the following values (y, x1, x2, w), where y is the measured quantity, x1 and x2 are the two ...
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Error Propagation for Unbiased Means

I am reading through https://arxiv.org/pdf/1210.3781.pdf, and do not understand its derivation for propagation of errors with respect to means. According to the text, when trying to estimate a ...
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How do I propagate correlated errors numerically?

I'm facing an error propagation problem in fitting some experimental data. I have measured several quantities, $m_i$, and I know from theory that $\sum_{i=0}^{n} m_i = 1$. Each of the $m_i$ has its ...
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Propagation of Correlated Errors

Suppose I measure three values, a, b, and c. I know independently a+b+c = 1. a, b, and c all have some measurement error; i.e. you could have a = 0.5 +/- 0.1, b = 0.3 +/- 0.05 and c = 0.2 +/- 0.05. ...
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Propagation of Uncertainties nonlinear case

Hello, I tried really hard to understand this page from a university script but I am lost. I would be very grateful if somebody could help me. To be more specific: How do I get the solution for A in ...
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Calculation of error on x intercept

I have a question regarding the calculation of the error on the x intercept. The following equation represents the error propagation equation $$\sigma_f^2 = \sum{\left(\frac{\partial f}{\partial\...
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chaining confidence intervals from samples (with covid19 application)

I've been dealing a lot with covid19 related data and it seems a lot of the work seems to calculate confidence intervals and pValue just for the step of the work they did while taking the previous ...
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Standard error vs error propagation

I am trying to work out the error on the x intercept of a graph and am slightly confused as to how I should go about it. Should I use the standard error on there mean or propagate the errors via the ...
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Which is the error of a value corresponding to the maximum of a function?

This is my problem: I use data observed with MUSE (which is an astronomical instrument provides cubes, i.e. an image for each wavelength with a certain range, link ) to extract a measure of redshift. ...
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Extract a mean and an error from different measurements

I have the following values from several measurements (they contain both systematics and statistical errors): $25.885\pm 1.851, 26.139\pm 0.979, 27.404\pm 2.049, 30.230\pm 6.729$ If I do a simple ...
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Uncertainty on fraction of a population

I have a sample (let's assume it unbiased) of the US population. The sample size is N and the number of people having a certain feature in the sample is n. I would like to calculate the uncertainty ...
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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 ...
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Average of two correlated variables

I'm studying tension versus time in a RL circuit with a square wave tension source. I have two sets of data: voltage across the resistor and across the inductor. I know the period of the generator, ...
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How error affects maximum detection?

I have a discrete function $f$ which lies over a certain domain $X$. My goal is to find the value of $X$, $x_{max}$, for which the function is maximum. I have opted for a simply search: using numpy ...
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Error propagation: when should I introduce self covariance?

I have a function $z_{ik}$ dependent from $x_{ij}$ with this form: $z_{ik}=(\sum_j x_{ij}\alpha_{jk}) \cdot ((\sum_jx^2_{ij})\beta_k)^{-1/2} $ for $i \in [1, N]$, $j \in [1, M]$ and $k \in [1, L]$ ...
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Error propagation of squared function, insert or not the self-covariance?

As my question suggests, I'm estimating the error of $z=x^2$. The general error propagation formula for two measures $x$, $y$ with errors $\sigma_x$, $\sigma_y$, is: $\sigma^2_z = (\frac{\partial z}{...
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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 ...
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Mean squared error increases during first epochs, then decreases rapidly. What can I infer from this data?

I've designed a vanilla backpropagation neural network and I am testing the various parameters to see what is ideal and look at the graphs to get some insight on how accuracy changes over time. The ...
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Regarding Norm-RMSE Computation

I am saying the above equation a Norm-RMSE. Here I am normalizing the deviation of each data point with respect to the actual value of that data point. Can I call it a norm-RMSE?? It also a kind of ...
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Error propagation through a calibration curve

Say I have a linear fit given y = ax + b. I'm given Δa and Δb as 95% confidence intervals. I now have several measurements y1, y2, y3, ... etc, from which of course I can gather a mean, standard ...
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Combining SE in X with fit error from linear regression

I want to map my predictor $X\rightarrow Y$ using linear regression, but I want to account for all sources of error. I have a standard error estimate for the predictor, $\textit{SE}_X$. The standard ...
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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 ...
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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 ...
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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 ...
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Calculate Uncertainty in Subtracting Part from Whole

Can you help me determine how to calculate uncertainty/variance for a particular scenario? I'm simplifying for the sake of simplicity, but let's pretend that we count the number of balls in a bag and ...
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How to calculate the standard error of a proportion estimate under misclassification?

Let's take a sample of size n from an infinite population. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would have $p =...
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mixing absolute or relative error with standard deviation for error propagation

I have an equation $$A = \frac{B \cdot C}{D}$$ where I want to know the error of $A$. As the variables are independent, the variance of this should be: $$\mathrm{Var}(A)=\sqrt{\left(\frac{\partial A}{\...
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Scaled covariance for error calculation

I am trying to do some fits (linear fits) and I just discovered (I am new to statistics) that most fitting programs have a parameter that can turn on and off the covariance scaling (e.g. in Python ...
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Error propagation with non-linear least squares

How do you take the variance of the datapoints into account to compute variance estimates of the parameters of a non-linear least squares fit? Suppose, I fit a non-linear model to a dataset $\mathbf{...
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How do I propagate asymmetric error/confidence intervals? [closed]

Assume that I have two measurements with asymmetric error, $X^a_b$ and $Y^c_d$, and I want to find $Z^e_f = X^a_b + Y^c_d$. How do I find Z? The type of answer I'm looking for is of the form : $e = ...
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Error propagation of measurements in linear regression

I apologise in advance for not using the correct vocabulary. I have a set of independent measurements $p_i:=(x_i, y_i)$. Each point has a fixed uncertainty $\Delta_p:=(\Delta_x, \Delta_y)$ i.e. the ...
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Software or code for calculating automatically the propagation of uncertainty [closed]

When calculating the value of a variable that depends on the experimental values of other variables, $y=f(x_1,x_2,...,x_n)$, a usual way to calculate the standard error of that value is this one: $$ \...
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Propogating Standard Error through monte carlo? [closed]

I have a model that has a bunch of parameters that I experimentally determined the mean and accompanying standard error/STD. Because the model has some tricky terms in it I'd like to propagate the ...
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Find Error in the vertex of a fitted parabola

I have a set of data (a Cross-Correlation function) to which I've adjusted a parabola (using lmfit python package ), from the fit I got the values of the parameters and their error: (Model): $f(x; a, ...
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Comparing standard errors obtained from error analysis to calculated values

Say I have completed some error analysis on a function and determined that the error in a particular variable ought to be ± 0.05 m for a particular variable. If I had a dataset of measurements made of ...
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Error Propagation of standard devi

I have following problem: I do measurements with technical triplicates and biological dublicates. So I prepare the same sample two times and measure each one three times. This gives me an average ...
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error propagation calculation (including the error on a derivative of a function)

I am trying to calculate the error on these 2 expressions: $A$ and $\kappa$ for a small error on V (say delta V), where V is a function of R ( a polynomial function)and R is the independent variable. ...
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Error Propagation of a measurement into a 1/log(x) equation

I have the following equation: T(°C)=(-4800/((log(x)+log(0.5)-log(1))-5.711)), where x is my variable and it has an uncertainty associated with it. I wanna calculate the error of my temperature ...
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How should I calculate a confidence interval for a gap-filled data set?

I have a data set of half hourly CO2 and CH4 fluxes (emission/uptake) from a landscape along with a set of environmental variables (Photon flux density (PPFD), temperature etc.). I'm using Neural ...
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How to calculate errors for cumulative distribution function

I have some data points of the form $(x_i,y_i,\delta y_i)$, where $y$ are counts and the error associated to each $y_i = N$ is $y_i = \sqrt{N}$. I want to create the cumulative distribution of these ...
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Likelihood of an observation for a small sample size

I am trying to understand how much an observation is compatible with other data, given that the sample size of this other data is very small ($n=5$). In practice, I have several measurements: $x_{1},...
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Errors on the mean

I have some data points from a measurement of a given quantity, and each point has an error associated to it. I want to report as the final value the mean of the measurements, but I am not sure what ...
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CNN Backpropagation Clarrification

Hi I am just trying to make sure my understanding of backpropagation with CNNs is correct, specifically CNNs that have multiple filters in each layer. This is how I have implemented backpropagation ...
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Correct method for error propagation in pseudo-data approach (simulation) using model

I want to compute the error on the integral over experimental data $(y_i,\delta y_i)$ in a pseudo-data approach using model ($x_i$ are assumed to be known error-less numbers). If I were using direct ...
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How to combine standard deviation of natural log and division equation?

I have two variables X_m and Y_m that are the mean of two data sets with standard deviations x_s and y_s. The equation I need to use is: A = |ln( X_m / Y_m)| How would I go about obtaining the ...
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Estimating the variance of an unknown vector

Imagine I have an MCMC approximation to the joint posterior distribution for the elements of some vector $\overrightarrow{A}$, and I want to estimate the sample variance of $\overrightarrow{A}$. For ...
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MC error propagation of multivariate function with variables with non-gaussian distribution

I'm trying to determine the error of $K_p$ in the following: $$K_p=\frac{a^3}{P^2}$$ $a$ derives from $a/R_s$, of which I had previously sampled the distribution using a MCMC sampler (the algorithm ...
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Error Propagation through R2 score

The $R^2$ score is defined by: $$R^2 = 1 - \dfrac{SS_{res}}{SS_{tot}} = 1 - \dfrac{\sum (f_i-y_i)^2}{\sum (y_i - \bar{y})^2}$$ for my fitted values $f_i$ from my model I have error estimates $\...
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Scaling residual function with uncertainties in data

Reading over the docs for lmfit (https://lmfit.github.io/lmfit-py/fitting.html), specifically the "Goodness of Fit Statistics" section states the following: "Note that the calculation of chi-square ...

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