# Questions tagged [error-propagation]

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

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### The standard error of precision from the standard error of intermediate precision and repeatability of a analytical chemical method

A validation report of an analytical method (to determine the assay of a product) is given and the goal is to try to determinate the overall uncertainty of it. I started with calculating the standard ...
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### How to estimate Mean with Uncertainty of a selected sample from variable A, that occured when variable B met some condition?

I am trying to find the mean of a sample from time-series of variable 'A', consisting of all 'A' values that occured when the concurrent Variable 'B' met some condition. I know that the A measurments ...
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### Error propagation from P-V error to RMS error [duplicate]

I have a question about the Error propagation in RMS. My surface profilometer has P-V error with 100 nm (It follows gaussian distribution). And I investigate the z-axis positions of the object surface ...
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### Error propagation for inferential statistics?

Assuming we have two samples from two populations each containing 10 independent observations + standard deviation. How should I propagate the error of the measurements themselves into the sampling ...
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### Equivalence between CRLB and uncertainty propagation formula

I already asked this question in the "Mathematics" stackexchange, but apparently did not find the right audience, so I am duplicating my question here, hoping someone might be of help. My ...
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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 $$\... 2 votes 0 answers 17 views ### Can be the output distribution non-normal using the moment method? I want to study the uncertainty propagation through a nonlinear function Y = f(X). I am assuming that X is normally distributed and I am using the moment method approximating f(X) by its first (... 0 votes 0 answers 5 views ### How expressing within and between groups variability? I have a double question related with expressing the variability (as standard deviation) of a dataset. Let's say I want to give an average value of the nitrogen content in "fruits" (units: ... 1 vote 0 answers 38 views ### Propagation of uncertainty in a derivative of a function [duplicate] I've performed an ordinary least squares on a data set with one variable. For simplicity, let's say I've fitted a polynomial function$$f(x)=a+bx+cx^2+dx^3.$$I obtain the best fit and the standard ... 2 votes 1 answer 42 views ### Relative error on a log-log plot Since absolute error plotted on a log-log plot will result in asymmetric error bars, my understanding is that this would give a misleading view of the precision of a measurement. I can plot instead ... 1 vote 0 answers 22 views ### Estimating uncertainties in parameters from minimization of an expression I was curious if they are anything in the literature about estimating or propagating uncertainties when the desired result is from the minimization of an expression. I have several books on ... 0 votes 0 answers 17 views ### Uncertainty estimation with errors in x and y (error in variables model) Given I have a training dataset (x_i=x_i^*+a_i,y_i=y_i^*+b_i) with independent errors a_i and b_i and I train a parametrizabele model \hat{y}_\theta(x_i)=y_i^*. I know I could bootstrap the ... 0 votes 0 answers 14 views ### How to propagate errors from two sources Suppose I performed 10 measurements, and have the dataset: ... 1 vote 0 answers 31 views ### Fitting data taking into account for the spread in data, which are zero for some data points I'm trying to use scipy to fit a \tanh function to some data. The data is of the form (x_i, y_i) for i=1,\cdots,N, where 0\leq y_i \leq 1. I choose x_i to be linearly spaced, such that x_0=... 0 votes 0 answers 7 views ### Propagation of uncertainty - when is it necessary to go beyond first order? When random variables y_j are independent, there is a simple expression for the standard error, \begin{equation} \sigma_f = \sqrt{ \sum_j \left(\frac{\partial f}{\partial y_j} \sigma_{y_j}\right)} \... 0 votes 0 answers 9 views ### Error propagation through multiple fitting I have a collection of N sets of data (x_i, y_i) that I believe follow the model$$ y_i = a x_i $$where a(b) is a linear function of some parameter b that is known for each i. My process is ... 2 votes 0 answers 59 views ### Include confidence intervals of samples in nlme model I have a continuous response variable (leaf length), which has been repeatedly measured in 45 experimental plots over several growing seasons. My goal is to properly estimate at which day of the year (... 0 votes 0 answers 26 views ### Effect of Simulation Error on the Monte Carlo Estimator Given a random variable X with known pdf f and some computer simulation model g(x): \mathcal R \rightarrow \mathcal R, mapping samples x \sim f to a scalar metric g, we can estimate the ... 0 votes 0 answers 12 views ### Propagating (non-gaussian) uncertainty i was reading this blog post Propagating (non-gaussian) uncertainty on how to show region confidences of fitted models. The author uses random samples generated by mcmc samplers to produce different ... 0 votes 0 answers 40 views ### how to propagate uncertainty in probability values If you are modeling probability of events (eg classic dice rolls or coin tosses) but want to represent probabilities as normal distributions, how do you propagate the uncertainty from individual ... 0 votes 0 answers 42 views ### Prediction error after mean-centring/transforming/etc. input data? Suppose that I have a linear model of p parameters (f(p,x)) that I want to fit to my dataset using least squares. According to Wolberg (2006), the prediction error in \hat{y} can be calculated ... 0 votes 0 answers 14 views ### Is it possible to propagate asymmetrical error estimates? I have estimated the errors on some parameters with a Monte Carlo technique by minimizing the chi-square$$\chi^2 = \sum \sum (x_i-y_i ) M_{ij}^{-1}(x_j-y_j)$$with M being a covariance matrix that ... 2 votes 0 answers 35 views ### Measure of goodness of polynomial fit at specific points or weighted analysis? I have some astrophysics data of "particle density vs orbital position" of a moon that emits a lot of particles. My research deals with the intensity of the scattered light which is ... 0 votes 1 answer 28 views ### Incorporating denominator uncertainty into a proportion I am calculating an incidence risk (r): number of cases of a disease in a population over one year (c) divided by the total mid-year population (N).$$ r = \frac{c}{N} $$Let's assume that c is a ... 0 votes 0 answers 17 views ### 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.... 9 votes 1 answer 240 views ### 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 ... 1 vote 1 answer 65 views ### 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 ... 0 votes 0 answers 68 views ### 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 ... 0 votes 1 answer 42 views ### 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 ... 0 votes 0 answers 30 views ### 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 ... 1 vote 0 answers 42 views ### Error Propagation When "Finding" a Value in an Array (using np.where for example) Consider you are given a dataset with x, y and y_err where ... 1 vote 0 answers 28 views ### Error propagation in normalized data to be used for non-linear modeling I have been given data where the raw readings conventionally have the mean of "blanks" subtracted from every reading. Then the blank-subtracted readings are divided by the mean blank-... 0 votes 0 answers 74 views ### How to calculate standard error of mean concentration of samples with standard errors in each sample I've been surfing Cross Validated trying to find an answer to this question of mine, and I've found these posts: Standard deviation of mean of a set of numbers, which are imprecise, Standard deviation ... 2 votes 1 answer 80 views ### How do I perform error propagation of a polynomial function? I'm trying to perform error propagation for some photometry code I'm writing, but I'm having some trouble with it! I have a value x that I draw from a distribution with standard deviation \sigma_x,... 0 votes 0 answers 33 views ### How can I simulate uncertainty propagation I am learning about uncertainty propagation, but it is all very obscure and I am not sure I understand it very well. I have a couple of exercises, but I want to run some simulations just to make sure ... 0 votes 0 answers 48 views ### Error propagation of correlated variables I am trying to propagate errors of a process that involves division of correlated variables and then taking the difference of the quotients. According to An Introduction to Error Analysis by John ... 1 vote 1 answer 510 views ### Error propagation with covariance matrix I have two measurements X = x \pm \sigma_{x} , Y= y \pm \sigma_{y}, where x,y are the mean values of X and Y and \sigma_{x},\sigma_{y} are their corresponding uncertainties. The covariance ... 1 vote 0 answers 51 views ### 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 ... 0 votes 0 answers 38 views ### Prediction with uncertainty after least-square estimation I've fit a model (the solution to differential equations or some other non-linear functions) to observational data to estimate the best-fitted parameters and their uncertainty by least-square methods (... 0 votes 0 answers 252 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 ... 0 votes 0 answers 17 views ### How to propagate errors in Model Building? I have developed two maps using a predictive linear regression where each pixel represents a predicted value of biomass or volume. Next I want to use those predicted values of biomass or volume to ... 0 votes 0 answers 73 views ### error propagation to get confidence interval for relative risk when only standard errors for numerator and denominator are known? How do I calculate a confidence interval around a relative risk (risk ratio) when all I have are predicted values from a regression model and their standard errors? I developed a generalised additive ... 1 vote 0 answers 165 views ### Propagation of standard error of fit through to the average and standard deviation of replicates I am using an equation to fit measured data. I have measured multiple replicates for each condition, each of which is then individually fitted to this equation. Once the data are fitted I obtain a ... 2 votes 0 answers 93 views ### Finding the Errors to a System of Non-Linear Equations I have a system of three non-linear equations, each with a solution that has error associated with it. It looks something like this: Solving the system of equations should produce an error for the ... 2 votes 1 answer 117 views ### How do measurement errors propagate into Percentiles? I have a measurement systems that outputs X_i + dX_i measurements. I'm trying to figure out the most correct way of estimating quality of measured device. The relative error dX_i/X_i is normally ... 0 votes 0 answers 18 views ### Error propogation through standard deviation I am trying to determine the best way to propogate my error with two points if I want to either average or take the standard deviation of them. For example, lets say I have two points 10 +-0.5 mg/L ... 0 votes 0 answers 15 views ### Estimate errors of predictions of a model based on its metrics I have trained a classifier with some data and I was able to get, let's say, for two classes C1 and C2 a recall of R1=0.71\pm0.06 and R2=0.94\pm0.02 (with the errors originating from a repeated K-... 1 vote 0 answers 77 views ### Arithmetic with normally-distributed variables Suppose x \sim \mathcal N(\mu_x,\sigma_x^2) and y \sim \mathcal N(\mu_y,\sigma_y^2) are random variables, and suppose \mu_y is large compared to \sigma_y. I want to know about$$ z=\frac{x}{y^...
If $A = A_0 \pm \sigma_A$, $B = B_0 \pm \sigma_B$, and $f = \frac{A}{B}$, the normal error propagation goes like (following Wikipedia) \begin{equation} \sigma_f = \sqrt{\sigma_A^2 + \sigma_B^2 - 2\...