All Questions
Tagged with uncertainty measurement-error
35 questions
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Binomial Test for data with normally distributed messurement error
I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
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Calculate mean and standard deviation of the ratio of two dependent variables
I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
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Definition of Uncertainity
I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
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Calculate the average of absolute values of a measurement with a measurement error
I have a few parameters; each is measured imprecisely with a known but unique random
measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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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 ...
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Hypothesis testing using samples with different measurement errors/intervals
Are there generalizations of common hypothesis tests (e.g. t-test, mann-whitney) that can take into account different confidences in the sample measurements?
For example, if I have two sets of ...
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114
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Combining uncertainties in replicate measurements
I recently got some Uranium–Thorium dates back from a lab. They are reported with a ±2σ uncertainty. Several of the measurements are replicates from the same specimen. That is, a few pieces from a ...
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When to use standard deviation versus standard error in linear error propagation
I have a question about linear error propagation. Let's say that I want to use an equation to calculate n, where n = (PV)/(RT) (eq.1)
I only take one measurement of P, and one measurement of T, but I ...
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762
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How to compare two quantities with uncertainties?
I've got two instruments that measure one quantity. One of them is regarded to be more precise, therefore, I use this measurement as a reference. Then, I take two measurements of the same quantity ...
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155
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Least square fit for data with uncertainty [closed]
I have a set of data $\{x_i,y_i\}$ that came from my measurement, so each of them has some uncertainty. I wonder is there a method to fit them using a model (like Gaussian), while taking care of those ...
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Including Ground Truth Uncertainty in Measurement System
I think this might be a basic scenario but I still struggle to find an appropriate methodology for my problem. Consider the following scenario:
There is a small moving object on an $xy$-millimeter-...
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614
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Weighted least squares fit with measurement uncertainty
I work with geophysics and in my research, some processes are described by power laws
$$k=\gamma v^{\alpha} u^{\beta}$$
To find the indices $(\alpha,\beta)$ the equation is rewritten as a logarithm ...
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2
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Calculating uncertainties in low stats radioactive decay data (Poisson Distribution)
Info:
I have a data set of radioactive decays in 15s (to clarify, each point is just the number of counts in the last 15s, as opposed to the cumulative number of decays - since there is 3s of the ...
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139
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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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1k
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Finding most likely permutation
[Hoping that this is the right Stackexchange site; inspired from a true story seen at work]
Joe has a measuring instrument and $n$ objects to be measured (say, a scale and $n$ weights). He measures ...
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2
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Is a statistically significant difference within analytical uncertainty still valid?
The isotopic analyses of two tissues across 50 specimens showed a mean difference of 0.12 ‰. A Wilcoxon signed-rank test for paired samples indicated this to be statistically significant (Z: -2.515, P ...
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Ratios and proportions as predictors [duplicate]
I am interested in modeling a continuous variable (e.g., second language learners' English proficiency measured in TOEFL scores) as a function of a number of predictors some of which are continuous ...
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Including model uncertainty in non-linear least squares minimization
The problem
I have experimental data $Y$ with heteroscedastic and normally distributed uncertainties characterized by covariance matrix $C_{exp}$. I want to fit the data using model $F(X, \beta)$ ...
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How to perform regression on data with uncertainty?
There are many resources for linear and polynomial regression, but I have not seen any material where the data comes with its own uncertainty as it appears in the real world. I have n data points, {...
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116
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Uncertainty in measurement error
Imagine having a list of positions $\mathbf{x}$ and two different systems trying to estimate $\mathbf{x}$. One system is more precise than the other, and it will be used as ground truth. When ...
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How to account for experimental errors when computing the derivative of a Gaussian process?
When applying Gaussian process regression upon training data, the covariance function can be generally given in the form: $\Sigma_{i,j} = k(x_i, x_j) + \sigma(x_i) \delta_{i,j}$, where $k$ is a ...
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Reporting model uncertinty
I hope I'm using the right terms here. I've generated a statistical model (PLS regression) based on LWIR (8-10.5 micrometer) spectrum from some lab samples. This model predicts the concentration of a ...
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1k
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Individual data point variance and covariance
In the paper, "Data analysis recipes: Fitting a model to data" (Hogg, Bovy, Lang), individual data point variances are found and used for subsequent statistical analysis. The data and corresponding ...
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Uncertainty of a least squares fit with uncertain data
I often find myself with questions that vary along this theme, but the internet is so full of simpler cases that I can never find what I'm looking for. So this question is two-fold: a) what's the ...
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276
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Uncertainty Calculation when measurements are subject to a constraint
I would like to know how to properly propagate the errors on measurements where I know a constraint on the sum of these measurements.
Lets say I have a rod of length exactly 1 metre which I have drawn ...
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250
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estimate uncertainty of experimental data
I evaporate atoms in a vacuum chamber and use a quartz crystal microbalance to measure the deposition rate. Specifically, I measure the resonance frequency of the quartz crystal and use that to ...
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Error implies uncertainty or uncertainty implies error?
Just a question in terms of context:
Error implies uncertainty or uncertainty implies error ?
Say for example, when you are not sure about your measurement ( i.e. have uncertainty) then you ...
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Detection Fraction from Counting Experiment: Poisson or Binomial Uncertainty?
Suppose I have 100 objects. I have some "detection criteria" such that I can tell you that 25/100 objects have been "detected." Therefore, my detection fraction is 25%. Now, I want to derive an error ...
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Type B uncertainties and statistical analysis
In the Guide to Uncertainty in Measurement (GUM), two classes of methods to evaluate uncertainties are distinguished : a type A evaluation is a statistical method, applicable when a set of ...
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Find error on the inputs
Suppose that we have a model with an input and an output. The model is exact (no structural uncertainty). However there is an error in the output ( the error is detected from already given exact ...
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Calculating uncertainties for histogram bins of experimental data with known measurement errors
I have a set of experimental data (with each data-point having its own measured uncertainty), and I wish to produce a histogram of it. The x values of the edges of each bin are already defined. The ...
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What determines the precision of uncertainties?
What limits the precision with which you can describe the uncertainty of a measurement?
I will describe two examples that feel qualitatively different, but I am not sure if they are quantitatively ...
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396
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Errors vs measurement errors
I'm reading about how to fit a straight line with measurement errors in both coordinates ($x$ and $y$).
Let the true unobserved variables be $x_{t,i}$ and $y_{t,i}$ and the observed variables be $x_i$...
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Can I convert a covariance matrix into uncertainties for variables?
I have a GPS unit that outputs a noise measurement via covariance matrix $\Sigma$:
$\Sigma = \left[\begin{matrix}
\sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ \sigma_{yx} & \sigma_{yy} &...
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807
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How do I handle measurement error in sparse data?
Under-educated non-statistician seeks short-term relationship for very one-sided benefit.
System in question involves rocks and physical properties. Modelling bits of the earth typically means few ...
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