# Tagged Questions

Measurement error is the difference between a measured value of a quantity and its true value.

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### measuring errors of bias, dispersion and outlier rate

I fit different models to a sample of data using Bayesian statistics. I have obtained for each data point in the sample a posterior probability distribution. Assuming I know the true answers for the ...
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### Intuition: Why do I have to worry about errors-in-variables?

I've read that (ordinary) linear regression assumes that there are measurement errors in the dependent variable, but no measurement error in the independent variables -- and if I have measurement ...
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### Realistic measurement errors on simulated observations

I have a code that simulates stars in a galaxy, outputting positions and velocities. I plug this data into another code to do some further analysis. Normally you'd also put in instrumental errors of ...
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### Error measure and learning process - Stuck!

Problem : You have N data points y1 <= ... <= YN and wish to estimate a ' representative' value. 1) If your algorithm is to find the hypothesis h that minimizes the in sample sum of squared ...
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### RMSE - where this evaluation metric came from?

Does anyone know where this metric came from ? Can someone bring article references or something like this? Im actually wondering if there's any mathematical concept or any way to demonstrate ...
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### Evaluate “sampling error” due to lack of data

I'm working on a problem of evaluating the long term success of some investments in some companies around Europe. My problem is that I have the information, before the investment was done, of say 100 ...
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### Standard error of mean - under measurement error

I have two observations of a normally distributed random variable: X1 = 0.02 X2 = 0.10 Obviously the sample mean equals 0.06, and the standard error of the mean (SEM) is equal to 0.04. Now things ...
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### Regression with Independent variables accuracy rates

I have a linear regression model predicting Y from X1 and X2. However, from separate analysis in the past, the independent variables X1 and X2 are known to be accurate a% and b%. Is there a way to ...
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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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### Survey data with ranking measurement error

I run a survey. The participant should rank 10 items with weight 1..10. Unfortunately I did not emphasis enough that every weight can be used once. Now I have a mixed dataset. Some items are ranked 1....
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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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### Differential measurement error in the dependent variable when direction of bias is known?

I have a dependent variable that I know is measured with measurement error. The observed values are always going to be less than the actual values, and the magnitude of this bias is correlated with ...
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### Consistent estimation with observed values lower than actual values

Assume an IID sample of the form $\left\{ y^{r}_{i},\mathbf{x}_{i} \right\}$ (notice the superscript on $y$). The observed values $y^{r}_{i}$ are bounded from above by the actual, unobserved values ...
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### Distance error for object detection algorithm in point cloud

I have a point cloud that was produced with stereo camera. Because of stereo camera (central projection) the density of points drops with distance, so the point cloud has been "normalized" with a ...
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### Computing bias due to measurement error:

I'm currently doing an exercise and faced with the following question: We have the true form: $y_i=\beta_0 +\beta_1 d_i +u_i$ Where $d_i$ is a dummy variable. We have measured $d_i$ with ...
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### How can additional data with measurement error be used to improve the predicitve accuracy of a model on data without measurement error?

I have two data sets with 7 categorical variables. The first small dataset (100 samples) is the goldstandard and contains only values that are exactly like they are in the data. The second dataset ...
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### Relationship variance, accuracy, and precision?

I have built a measuring machine. It takes a photo of something and tells you how tall that thing is. I took three photos of the same object. On those three occasions, my machine said the object ...
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### How should the error-term in reporting results be properly written to make sense?

I want to report results obtained from a number of measurements with the average value plus minus the standard deviation. During my studies I was always thaught to use only one signifying digit in the ...
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### Testing significance of RMSE of models

I repeatedly trained two neural network models and calculated the RMSE for each run (split validation). Which statistical test is most useful in this case for testing if the difference of the models ...
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### Shouldn't the root mean square error (RMSE) be called root mean square residual?

As far as I understand, estimating the error of a model, say an artificial neural network, requires to know the "true" model. Wikipedia says in its article "Errors and residuals": "The error (or ...
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### Random Forest OOB error rate in R

I am building my model in R and am using the randomForest package. ...
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### Measurement errors

Let $n$ points $(x_i, y_i)\in \mathbb R^2$ satisfy $$ax_i + bx_iy_i + cy_i = 1,\, i=1,\ldots, n$$ Each point is observed with an error \$\boldsymbol \varepsilon _i = (\varepsilon _i^x, \varepsilon ...
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### Proper approach to Gamma-distributed data prediction with measurement errors in outliers

My task is to predict Gamma-distributed data with a large number of extreme-valued outliers caused by measurement error (i.e. the machine that records the values intermittently malfunctions). My ...
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### measurement accuracy relation to sample size

I am measuring the volumes of a number, n, of physical objects with an accuracy of +/- 2%. I would like to estimate the total sum of the volume of all n objects. Each object is similar, but not ...