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Questions tagged [error-propagation]

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

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Error propagation for cubic relationship

I have the cubic relationship between two variables, x and y, and I need to find the error in x. y = ax^3 + bx^2 + cx + d I have the values for the coefficients and their respective uncertainties. I ...
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9 views

Error propagation: estimating population mean from set of predictions

I'm trying to develop an efficient method to estimate the population mean. The most obvious way is of course to directly sample subjects and take the mean, but in this case that is sometimes not ...
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What is the difference between chi square and coefficient of determination (R square)?

What is the difference between chi square and coefficient of determination (R square)? What is their significance, limitations, and applicability as compared to another?
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43 views

Gaussian distribution with error in both parameters: trying to create a Gaussian distribution with no error in either parameter

I am trying to create a Gaussian distribution where the parameters are not precisely known. I have mean $\mu$ and standard deviation of the mean $\sigma_\mu$ (modeled as an uncorrelated Gaussian), and ...
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25 views

Uncertainty on integrated function fitted to data

I have some data that has been fitted with a function of several parameters (using scipy.optimize.curve_fit). The function describes a two-component spectral energy distribution: $$S (\nu) = \frac{2 h ...
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14 views

Standard error of the mean and fits

I am trying to understand what kind of statistics I should use to correctly report a mean value. Essentially, I have a number of curves that belong to the same population, and I use the same model to ...
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28 views

Propagation of uncertainties in correlated measurements (Inverse of a measurement)

Suppose that you have $n$ uncorrelated measurements $A_{1}= a_{1} \pm \sigma_{1}$ , $A_{2}= a_{2} \pm \sigma_{2}$ ... $A_{n} = a_{n} \pm \sigma_{n}$, where $a_{m}$ is the mean value of $A_{m}$ and $\...
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7 views

Uncertainty when taking the difference between a measurement and a subset measurement

Lets say I collected $\mathbf{N_t}$ data points for an experiment and this resulted in a measurement of $A\pm\sigma_A$. Then I'm interested in how a particular variable effects the study and remove $\...
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13 views

How to conduct error propagation for an uncertainty budget?

At my job I'm attempting to build an uncertainty budget for an experiment in which repeated measurements of multiple elements' masses were taken. Then I am finding certain mass ratios. I calculated my ...
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26 views

How to include standard deviations in diversity calculations?

I have community abundance data where each species has a mean and a standard deviation (determined by replicate samples). I am comparing the diversity of two communities. The various diversity metrics ...
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41 views

Error Propagation through Iterated Functions (variable star data)

I'm an astronomer trying to smooth variable star data, and one way I'm doing this is using a 7-point, second-order Savitzky-Golay filter. I iteratively apply the filter 51 times (i.e. I apply the ...
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11 views

How do I propagate error on parameter fittings where the observations also have uncertainty?

I have a model that takes in a pressure $p$ and returns a concentration $C$ and uses three fitted parameters $C_H^{'}, b,$ and $k_D$. The function (for completeness) is $c = k_D\cdot p + \frac{C_H^{'}...
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Propagation of uncertanty with an example

I'm following a Regression and Other Stories book and exercices proposed. Do you agree with my proposed resolution? Unfortunately i've no solutions reference to verify if my calculation is correct. ...
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15 views

Average of compound value or compound of averages?

Suppose I'm measuring the flow rate of a tube. I measure the time it takes to fill it twice. Each time, I also measure its final volume. So what is the best approach to calculate the average flow? ...
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1answer
29 views

Log and exponential uncertainty propogation

I am processing data on a radioactive decay experiment, and need to find the errors on some quantities that I can get from some fit parameters. I would like to obtain: $\sigma A$ from $A = e^{a}$, ...
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6 views

Error propagation for parameters of multiple similar fits

I have a set of similar, uncorrelated measurements, each containing a few data points like the following: The quantity of interest is the slope of a linear model ($y = mx + b$) that is fitted to each ...
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Median error propagation

Assuming we have a set of measurements $x_i, i=1,\dots,N$ each with an error of $\Delta x_i$, I then normalize the data by the median of $x$. Can an error for the median value be calculated with the ...
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The difference between a standard error and a propagated error

I'm confused about the difference between the standard error and the propagated error. For example, say that I got two measurements which I want to average: $16.04 \pm 0.31$ and $15.72 \pm 0.28$. The ...
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Estimate Variance-Covariance matrix via Error Propagation of Weighted Least Squares Equation

Given a linear system $b_{obs} = Ax$, how can I derive the covariance of $x$ (i.e. $C$) from the weighted least square solution equation: $$x = (A^TS^{−1}A)^{-1}A^TS^{−1}b_{obs}$$ With $C$ being the ...
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1answer
30 views

How to report a +/- standard error for logarithmic data?

I have some data $y$ which varies logarithmically which I am fitting with MCMC methods. It makes more sense to do my analysis in the logarithmic space $z = \mathrm{log}(y)$. As I result, I end up with ...
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51 views

Taylor expansion of Gaussian process function with input noise

I am reading "Gaussian Process Training with Input Noise" by Andrew McHutchon and Carl Edward Rasmussen, where it is assumed that the inputs $x$ are noisy measurements of the actual latent ...
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19 views

How do I "propagate" the covariance?

I have two measurements, $X\pm\delta X$ and $Y\pm \delta Y$, and their "measured" covariance $\mathrm{Cov}[X,Y]$. (My case is that $\mathrm{Cov}[X,Y]=0$, but I want some general formulation ...
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Calculated standard error of two covariant variables of different weighting schemes

I have two variables $\bar{X}$ and $\bar{A}$ calculated as $\bar{X}=\sum_{i=0}^{n}w_{x,i}x_i$ where $x_i=i$ and $\bar{A}=\sum_{i=0}^{n}w_{a,i}a_i$ where $a_i=i$. From there $s_A$ and $s_X$ are then ...
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1answer
46 views

Adding of two confidence intervals

Given two variables $\bar{A}$ with 95% confidence interval [$A_0$,$A_1$], and $\bar{X}$ with 95% confidence interval [$X_0$,$X_1$], how would one calculate the 95% confidence interval of a composite ...
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1answer
45 views

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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11 views

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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43 views

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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39 views

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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1answer
43 views

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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23 views

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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1answer
89 views

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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1answer
83 views

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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51 views

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
21 views

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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1answer
27 views

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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30 views

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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1answer
217 views

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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18 views

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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14 views

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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31 views

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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28 views

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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15 views

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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1answer
35 views

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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