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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18 views

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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21 views

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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43 views

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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2answers
115 views

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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15 views

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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51 views

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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1answer
47 views

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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16 views

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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23 views

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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1answer
70 views

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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10 views

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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1answer
15 views

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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14 views

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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18 views

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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12 views

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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12 views

Combined measurement uncertainty for mass computation

Problem I would like to determine the combined standard measurement uncertainty for a mean mass $\bar{m}$ computed from a mean volume $\bar{V}$ and a constant density $\rho$ with $\bar{m} = \bar{V} \...
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1answer
126 views

“cumulative” vs “additive”

I was reading a brief theory of measurement from ftp://ftp.sas.com/pub/neural/measurement.html when a passage got me stuck. It says that Consider a rat in a Skinner box who pushes a lever to get ...
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15 views

Error propagation: add errors in quadrature, or use a weighted standard deviation?

I have a measurement $x$ with a known uncertainty $\sigma_m$. I have a black box that can take an error-free measurement $x$ and produce a value $y$ with a known uncertainty $\sigma_{b}$ (which is ...
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1answer
17 views

Combining measurements with known uncertainties

I have $N$ rulers that each have a different but known level of accuracy, e.g. one's a meterstick, one's a yard stick, etc. I measure the length of my table using each ruler. How do I combine ...
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1answer
23 views

What method for forecasting error measuring in a poisson process?

There's so much different measures for the forecast error that I kind of lose the sight on which one to use. Out of the following: MAPE, ...
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2answers
143 views

Propagation of uncertainty through a linear system of equations, Ax=b, where A and b are correlated

I have a linear system of equations in the form Ax = b. The elements of A and b were experimentally determined and as such have some uncertainty. Within each row, A and b are correlated. Between rows, ...
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10 views

Propagation of errors including deviations

I have $n$ experiments, and for each experiment $i$ there were a variable number $m_i$ of measures $y_{ij}$ taken, which were combined resulting in a single measure $x_i = \frac{\sum_j y_{ij}}{m_i}$ ...
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28 views

The effect of Measurement error on a Beta Coefficient

I am trying to show the bias of the slope coefficient that occurs when there is measurement error in the regressor. $$ Y = a + B* x_{i} + e_{i} $$ To find the beta coefficient, we can use the ...
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39 views

How to calculate the per-pixel uncertainties of an image after convolving it with a 2D kernel?

I have one 2D image (let's call it "model image"), which is generated by evaluating a particular analytic model for each of its pixels. Since this is just a simple analytic model, there is no error/...
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43 views

Chi square statistic when both model and data have errors

I have written a code which fits a model to some data. My model and data are two-dimensional images. To be more precise, I am fitting some kind of galaxy model to astronomical observations. The ...
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22 views

Error calculation from calibration data?

Suppose I have the following calibration data from a measuring instrument: ...
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59 views

Why is my R-squared so low when the relative absolute error is not that bad?

I feel this may be a slightly dumb question but I'm trying to predict the price of a good and I'm obtaining low r-square values (approx. 0.20) but, in my case, acceptable absolute relative error (...
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30 views

error measurement bias in dependent variable correlated with both the dependent and the independent variables

I have to estimate a model where because of a transformation of the dependent variable I now have a measurement error in the dependent variable that looks like Y^_i = Y_i (1+h_i). The reason why this ...
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2answers
56 views

Is CFA appropriate for test retest reliability?

I know CFA is often used when there is a latent variable that has measurement error that can attenuate correlations. However, does it make sense to make this same adjustment for measurement error when ...
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1answer
96 views

Converting between different accuracy/error metrics

I am trying to compare model accuracy between several different measurement metrics. For example, some citations use accuracy while other use error. That one is rather obvious, but there are lots of ...
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1answer
60 views

Measurement error in independent variable may not really matter?

In OLS, since measurement error in an independent variable biases its coefficient toward 0, if the coefficient ends up significant (with the expected sign), then is it true that the measurement error ...
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14 views

Precision of bone density measurement

I just did a precision study scanning 30 patients twice. The calculator presented the least significant change score, but how do I calculate my precision? For instance, the ISCD states that the ...
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98 views

Meta-analysis using experimental reliability data

I have a rather conceptual question. We measured experimentally the reliability of a certain readout. Now what I would like to do is to use this data to give a statement about the results of previous ...
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15 views

Detect grid in 2D plane

Given is a set of points (x,y) in a two dimensional Cartesian coordinate system. Many points are near the crossing points of an affine transformed grid. The points have been measured and may have: ...
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23 views

Calculating error in hourly/daily/annual duplicated observations

I'm hoping to determine the best way to describe and quantify measurement error in a salmon counting project I work on. Here's a description of the setup: Salmon passing upstream pass through a pair ...
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2answers
36 views

Adding Up Margins of Error

I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same ...
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37 views

Which statistical method should I use to compare test results of two groups with each other and with exact values?

I am currently working on an in-vitro medical device for an academy project with my teammates to see if our approach to a certain problem is working. We are hiring two groups of volunteers (15 people ...
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59 views

Bayesian Linear Regression for Noise-Free Data (using PyMC)

I was surprised to find out that fitting a straight line into "perfect", i.e. noise-free, data, results in rather large uncertainties for the estimated parameters. Example and Estimation Results ...
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11 views

Multiplicative Measurement Error in Response Variable

I understand that taking log of the multiplicative error model transforms it into the additive error model. Let $y'$ be the observed response variable, with $y$ being the true response variable and $\...
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3answers
149 views

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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24 views

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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1answer
299 views

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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65 views

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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157 views

Random Forest OOB error rate in R

I am building my model in R and am using the randomForest package. ...
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40 views

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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36 views

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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15 views

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 ...
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6 views

Measuring / Characterizing error in ordered data

I have two sets of data points. The ground truth set and the measurement set. The magnitude measured is time, and it is important that each data point in the measurement preserves the order in the ...
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36 views

Measuring Prediction vs Actual Difference

To find error we usually measure our predicted y vs actual y. Are there any error terms that measure the error in y AND the error in x, given y? In the image below the line is doing a pretty good ...