Questions tagged [error-propagation]

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

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likelihood as random function wrt data

Suppose we have some dataset $x= \{ x_1, \dots, x_n\}$ where every datapoint is i.i.d., $x_i \sim P(\cdot|\theta^*)$ for some known distribution $P$ and true parameter $\theta^*$. Then, for this ...
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Applicability of Gaussian error propagation for poissonian distributed data

my question is whether there is an analytical expression for the error on a function where the variables of the function all follow a Poisson distribution? I will give a coded example with ...
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Method comparison (e.g. Bland-Altman) for new method vs. reference with known error (silver-standard) relative to gold-standard

I would like to know how to adjust agreement measures to estimate candidate method agreement with a gold-standard method, given results of a candidate vs silver-standard test, where the silver-...
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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 ...
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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 ...
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Can I use a correlation matrix and variances to find the covariance matrix? [duplicate]

I want to calculate error propagation of the non-linear $A\times B$ function, where $A=a+\sigma_A$ and $B=b+\sigma_B$ are two correlated random variables, using toy MC. I am lost as to how one finds ...
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Extracting a measurement from a line fit given error on its parameters

Say I have some data that follows a linear model. I fit a straight line through it, and obtain best fit parameters $m$ and $b$ with an error $\delta_m$ and $\delta_b$ associated to them. Say I wish to ...
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Linear regression on data with associated errors in the x and y direction

I have experimental data that I need to linearise in the form $\ln(b/x)$ vs. $x$, where $x$ is an experimentally-derived quantity and the value of $x$ is dependent on $b$ (which varies). $x$ has some ...
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How to calculate the “cumulative” standard deviation

I have gridded spatial data. The data is 30-year averaged climate data and has units of mm/yr and an associated standard deviation for that grid cell. For example, a grid cell has a value of X mm/yr, ...
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Estimating the errors in parameters in the ordinary least square

I am reading the book An Introduction to Error Analysis by John R. Taylor. In Ch8: Least-Squares Fitting, he has derived expressions for parameters $A$ and $B$ in fitting the line $A+Bx$ to the set of ...
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Calculating error from covariance of graph and errors of data?

I have some data, with known error, and have used a linear regression algorithm to make a fit of this data and plot it. I have also used the algorithm to calculate an associated covariance. How would ...
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Covariance matrix of element-wise quotient of two sets of measurements with known covariance matrices

I have two sets of measurements, $x_i$ and $y_i$, both with the same number of elements, $N$. For each of these sets, I have known $N\times N$ covariance matrices, $\Sigma_x$ and $\Sigma_y$, ...
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How do I calculate error margins for difference in proportions?

I have data that captures responses to stimuli and categorises both the cue stimuli and response stimuli for both male and female, as follows: Cue Stimulus Response Stimulus Gender Cue Count Cue ...
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1answer
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How do I determine the error propagation of my table?

I have different predictions for the future (table below). These two predictions V1 and V2 are both telling us something about ...
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How do I find std.error with error propagation and for extrapolated data?

I have a table with different means. Some of the data is predicted future change, and the rest I have extrapolated. ...
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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 ...
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Confidence interval for linear combination of regression coefficients that are calculated from different variables

I would like to estimate a confidence interval for a linear combination of regression coefficients that come from several linear regression models that are calculated from different but correlated ...
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Jackknifing a multivariable statistic f = f(x,y,z) with different sample numbers for variables

I have a dataset consisting of three variables $x = (x_1,x_2,...,x_{N_x}), y = (y_1,y_2,...,y_{N_y}), z = (z_1,z_2,...,z_{N_z}) $, assumed to be independent. I need to compute two statistics from this ...
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Error propagation in intersect of line and regression line: at each step or the full expression?

BACKGROUND I am a PhD working with physics measurements, each with measurement uncertainties attached. A measure of central tendency is found using a model specific to my field. The output is a ...
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Error Propagation and CV?

I would like to know if someone can help me with basic statistical questions, please. I read in many documents on the internet that if I want to calculate the mean of two values, where each value has ...
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making a single prediction based on multiple predictions with associated uncertainties (eg ensemble models)

Let's say I have a set of predictions $y_i$ and associated uncertainties $\sigma_i$ and the predictions are all normally distributed. How can I "add" these up to make some final prediction. ...
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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://imgur.com/a/plW6t83) The parameters Tc, T0, Zb and Z0 are fixed. hr is normally distributed K is normally distributed in log10 ...
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Someone help me with error propagation? [closed]

I have a fraction: $y = (A/B)-1$, where $A$ and $B$ are values (constants) with an associate value of error. How do I calculate the error of each $y$? And then I have to plot the average value of my ...
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Determine influence of uncertainty of X on Y

I made a measurement in the lab by measuring Y ~ X with the help of a very precise lab measurement device. Unfortunately, I cannot reveal the meaning of it though I ...
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Trying to calculate error for equation with dependent variables

I have the following equation for which I am trying to calculate the error in: $$v=b+c/t$$ $t$ is error-less but $b$ and $c$ depend on each other and therefore I cannot use the standard addition in ...
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Combining Error Terms into a General Error Term

Lets say I have 4 error terms: $$e_1,e_2,e_3,e_4$$ Each of these error terms come from different simulations of data using different classification methods. Let $\gamma$ be the number of empirical ...
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Uncertainty of a Mean from measurements with different uncertainties and of different items

I've searched around, but I am just not sure that the explanations I've found quite match up with what I am trying to do. Let's say I have 3 vials of a gas. For each vial, I measure some $T$, $P$, and ...
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What statistical metrics / tools can be used to quantify underestimation of uncertainties in distances to astronomical objects?

Amazingly low uncertainties are frequently reported in distances to astronomical objects. However, the uncertain region of the measurements frequently fail to overlap. Is there a statistical measure / ...
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Uncertainty propagation for correlated variables

The following is a toy problem to illustrate my question. Let $[A_{1}, ... ,A_{n}]$ be a series of $n$ random variables. Each variable has $m$ observation under two experimental conditions resulting ...
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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 ...
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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,...
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48 views

Error for operations for Two Poisson distributions

Can error (std dev) in A +B or A-B be $\sqrt{A}$+$\sqrt{B}$ if A and B are Poissonian? If yes, what would be similar expressions for AB and A/B ?
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Is there a way to estimate the error of a measurement based on it's effect on a dependent measurement?

I know the title is vague but I don't know how to phrase it better in one line. I have a measurement of a consumption process that should be linear based on the amount of cells present in my ...
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Expression for the variance of the slope between two measurements

Let's say we measure two points $S_1$ and $S_2$, at $x_1$ and $x_2$ respectively. $S_1$ and $S_2$ are contaminated with Gaussian noise with standard deviation $\sigma$. We now want to calculate the ...
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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\{(\...
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Error in Gamma Ray data: chi square value

I have Gamma-ray data for which I am fitting the stars with a constant (one parameter) first to remove the unwanted or garbage data. I plotted counts vs MJD value. For this data as Poisson, the error ...
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Standard deviation/variance for the sum, product and quotient of two Poisson distributions

What would be the standard deviation for $A+B$, $AB$ and $\frac{A}{B}$ for $A$ and $B$ Poisson distributed?
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What's wrong in this derivation of back-propagation errors?

I'm trying to find a rigorous derivation for the backpropagation algorithm, and I've gotten myself into something of a confusion. The confusion comes from when and why people transpose the weight ...
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Error propagation in an equation without an analytical solution

Is it possible to formally propagate uncertainties through an equation which does not have an analytical solution? I am an Earth Scientist working on doing a rigorous determination of the age ...
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1answer
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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 ...
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Correct way to combine 95% confidence interval bounds returned by a fitting routine with several measurements?

I am looking for someone to just confirm / double-check something for me with regards to errors on measurements. Let's say I am trying to determine the slope of a relationship by varying one quantity ...
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Error analysis in sampling multivariate distribution

Consider a discrete joint distribution $p(x_1, x_2, x_3)$ over variables $x_1,x_2,x_3 \in \{0,1\}$. By the chain rule of probability, the following algorithm samples correctly from the joint ...
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How do the errorbars change when time series is mean subtracted?

I want to subtract the mean from my time series. Each data point has a corresponding errorbar. I calculate the mean by fitting a constant with a MLE estimation and estimate the standard error with the ...
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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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1answer
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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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