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Questions tagged [measurement-error]

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

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Historical Curiosity - Endogeneity Problems

Before Philip G. Wright proposed in 1928 the method of Instrumental Variable as solution endongenity problems, How did Econometricians and Statisticians solve economics models with endogeneity. ...
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measurements with gaussian error

I'm reading a printed document(learning material) which says "Person A made measurements of a quantity, with Gaussian errors". To me this expression seems odd and the meaning is unclear. Is that a ...
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How do I tell if the sensors that feed a Kalman filter has diverged?

I have a time varying variable $x$ that I want to estimate. I have two sensors A and B that measure $x$. I feed their measurements to a Kalman filter. Sometimes, one of the sensors degrades for a ...
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Measure effectiveness of algorithm (plot included for clarification)

I have written a short algorithm that computes the "comovement" of a time series. My problem is what method to use to measure how accurate this algorithm is. Ideally it should only have negative lines ...
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Performance Imbalance Dataset Decision Tree

I have a imbalance dataset for a classification task, with the minority class accounting for about 21% of the total. When I use a decision tree based model for prediction, let's say a classification ...
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Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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Deterioration of the accuracy of a system over time

I have a system that compares the predicted variable with the true variable by calculating the absolute error percentages. . Where $\pi$ is the predicted variable and P is the true variable. And you ...
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How to find the standard error of a sample of measurements each with their own uncertainity

I have a scale that has a resolution of +-0.01 grams. I have assumed that it has a standard error of +-0.005 grams. I would like to measure the mass of an Samsung INR18650-30Q battery. I would like to ...
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Which approach should be used to compare two different measurement techniques of same samples?

I have individually measured failure forces of 8 materials and those recorded with A method and B method in same time: 8 results in each method, A=8 and B=8. The range of data of both measurement ...
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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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1answer
14 views

Correction for measurement error

Let's suppose that the true model is: $$ y_t^* = x_t^* \beta + e_t^* $$ and suppose that data on $x_t^*$ is observed with error: $$ x_t = x_t^* + u_t $$ If we consider the regression $y_t^* = x_t \...
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Does the RMSE formula have a $k$ in the denominator?

In what circumstances does the RMSE formula have a $k$ in the denominator? StackOverflow's What does RMS stand for? shows this formula for RMSE: $$RMSE=\sqrt{\frac1{n-k}\sum_i(y_i-\hat{y}_i)^2}$$ ...
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Berkson versus classical measurement error: how to choose?

When discussing the consequences of mis-measured variables, an important distinction is to be made whether the measurement error is of the classical, or Berkson type: Classical: $x=a^C + b^Cx^{*}+e$, ...
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Corrected Standard Deviation for Differences in Means

In the published work of Altman and Bland: Statistical Methods For Assessing Agreement Between Two Methods of Clinical Measurement, Lancet 1986 (https://www-users.york.ac.uk/~mb55/meas/ba.pdf) , page ...
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Covariance of measurement uncertainties

So I have a sample of data points call them $X_1$ and $X_2$, these are derived quantities based on measured values and each has a mean $\mu_{X_{1,2}}$ and variance $\sigma^2_{X_{1,2}}$ which can be ...
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Determination of MPE (maximum permissible error) in CMM

Which approach should I use for evaluation of MPE (defined in ISO 103600)? MPE is a characterization stated by the manufacturer of a length measuring device (coordinate measuring machines). It says, ...
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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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Linear regression where some known records have a measurement error in dependent variable

I am modelling data where the dependent variable is the number of units of a certain product sold each month in each area. In all areas, the product is sold by a chain of shops 'A' and we have exact ...
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Median Absolute Deviation

How median Absolute deviation is immune to outliers? R2 or coefficient of determination is affected by outliers. And how this MAD is going to remove that constraint?
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Combined uncertainity given probability measurement belongs to one of two classes

I have two classes of measurements $A$ and $B$ characterized by different uncertainty distributions. I also have a probability $P_A$ that a given measurement belongs to class A and not B ($P_A = 1 - ...
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1answer
25 views

Is non-sampling error included in hypothesis testing assumptions?

I understand that, in hypothesis testing, we are dealing with sampling error. We calculate the statistic from the sample data and test what the probability of getting that result is when the null ...
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Which correction do I need to get a measurement uncertainty from the sample standard deviation?

I'm an experimental physicist who mainly needs statistics for the calculation of measurement uncertainties and confidence intervals. Since my results are usually normally distributed, I simply take $N$...
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When making a fit to data without weights, how reliable are the fit errors?

I often need to fit data which is a spectrum. And it isn't possible to have many identical spectrum from which to produce error bars on the individual points in an averaged spectrum. So my question ...
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Does this mean my model is useless?

Long story short, I have a random forest I've created. It's mean absolute error is .209 for the test set. The (scaled) standard deviation of the y column is .201 (for all the y column data, not just ...
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Using regression weights when $Y$ might be measured with bias

Suppose we observe data $Y, X$ and would like to fit a regression model for $\mathbf{E}[Y \,|\, X]$. Unfortunately, $Y$ is sometimes measured with a systematic bias (i.e. errors whose mean is nonzero)....
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Asymmetric error measure for forecasts

I am building a model for forecasting some number of activations. My data set has a panel structure. Now, I want to come up with a forecast performance measure to assess the performance of my model ...
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Does the size of original dataset influence measurment error in bootstrap? [closed]

As above. So for example would the measurment error of model's r-squared be higher if the bootstrap sample (1000) was drawn from original sample of 20 observation than if the bootstrap sample (1000) ...
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1answer
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What is the error of my regression? [closed]

I'm conducting a polynomial of a third degree upon a diode measurement where Amplification was measured against Voltage. It's a very exponential behavior. However, I used the ...
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66 views

ARIMA model with measurement error

I'm interested in forecasting a time series $m_t$ which is contaminated with measurement error $e_t$, so the observed time series is $y_t = m_t + e_t$. I can suppose $m_t$ and $e_t$ are independent ...
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Identifying problems in psychometric data set

I am analyzing the data from two questionnaires designed to measure the same trait which are highly correlated with one another and have very similar questions. My data is from one group which ...
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1answer
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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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1answer
32 views

Predicting proportion of individuals belonging to different classes

I am trying to compare performances of different classifiers to predict some data. The variable I wand to predict is binary (A or B), and I have a bunch of predictive variables to predict to what ...
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Adjust intraclass correlation for measurement error

It's been known since Spearman (1904) that one can adjust an observed Pearson correlation for measurement error using this formula (R code with tidyverse attached): ...
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Optimizing $\chi^2$ using MCMC

I have measurements of an object. Let's say I have its length $L$, mass $M$, and age $t$: $$\mathbf y = (10~\text{m},\ 0.01~\text{g},\ 5~\text{s}).$$ I also have the uncertainties on my measurements ...
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1answer
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Is the loss is the same as the error in deep learning?

Is the loss is the same as the error in deep learning? I feel it's the same but I'm maybe wong...
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1answer
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Propagation of uncertainty when summation symbol is involved

I am unsure how to estimate the propagation of uncertainty when there is a summation symbol involved. I have the formula (its used to calculate the sauter mean diameter but I will give a simpler ...
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1answer
109 views

Estimate signal-to-noise ratios by regression

Suppose we need to measure $y^*_i$ where $i=1,...,n$. We have two independent noisy measurements, $y_{1i}=y_i^*+\xi_i$ and $y_{2i}=y_i^*+\eta_i$, where $\textrm{Cov}(\eta_i,y_i^*)=\textrm{Cov}(\xi_i,...
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Sample Size Adjusted Metric for Calibration Curve

I'm creating a model that provides a predicted probability of an event happening. I am using calibration curves that plot predicted probability (x-axis) versus the actual event frequency (y-axis). I ...
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1answer
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Standard error of mean vs error propagation

I'm confused on how to correctly calculate the final uncertainty from averaging measurements that each have their own internal errors. Say I have 3 voltage measurements: (1.232 ± 0.001) V, (1.197 ± 0....
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Deconvoluting an ECDF via mixed modeling

I have data with measurement error, $W_i$, with the following structure: $$W_i = \mu + \gamma_i + U_i$$ where $U_i \sim N(0, \sigma^2_i)$, with known $\sigma^2_i$, and $U_i \; \amalg \; \gamma_i$. I ...
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1answer
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Using datapoint multiple times in error [closed]

For a simple regression problem, say I have a function $f = x^2 + ax$ and am using mean squared error as a loss function. In each calculation of mean squared error, each datapoint gets used twice (...
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Probability distribution of actual value based on observed value with error relative to the actual value?

I use a method of estimation (a variant of HyperLogLog) that estimates cardinality of some set with a "relative error". Let's assume $$\hat{\rho} \sim \mathcal{N}(\rho,(\rho c)^2) $$ where $\rho$ is ...
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Distribution of extremes of measurments considering repeated measures

I'm working with measurements for a large sample set and need to quantify the expected extremes. The measurements obviously have some degree of random noise simply in the measurement itself (for the ...
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One-sided measurement error: $\widetilde{X} = X - \eta$, $\eta\geq0$. Is $E[X|\widetilde{X}=\widetilde{x}]$ increasing in $\widetilde{x}$?

Let $X\geq0$, $\eta\geq0$ and $X,\eta$ independent. We measure $X$ with a one-sided error: $\widetilde{X} = X - \eta$. Is $E[X|\widetilde{X}=\widetilde{x}]$ increasing in $\widetilde{x}$?
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Is the error rate always the Bayesian one?

I know from Wikipedia that the Bayes error rate is: $${\displaystyle p=1-\textstyle \sum _{C_{i}\neq C_{\text{max,x}}}\int \limits _{x\in H_{i}}P(C_{i}|x)p(x)\,dx}$$ where $x$ is an instance, $C_i$ is ...
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Measure of error for non-linear systems?

I am trying to model a system that is ideally explained by the formula Q=Qi*(1+Di*b*t)^(-1/b), where: ...
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1answer
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Can I roll-up forecasts to analyze against benchmark methods?

There's a software product (call it Main) we use to allocate parts to various locations. The way it works is it sums up the demand history of all locations to the part level. For example, if part A ...
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Assigning Error Bars On Extreme Measures

Extreme measures require principled quantification of the error bars on such measures because of sample size limits. A statement like "90% of scores will fall between X and Y." is of a different ...
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reconstruction loss for disentangled variational autoencoders

I am using disentangled variational autoencoders which is a variant of VAE. You will find the github code in this link. I want to quantify the difference or the loss between the ground truth (...
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Can total least squares be used to account for uncertainty due to measurement timing?

Suppose we have a dataset in which we wish to perform regression analysis, and where the response/dependent variable is a measurement at time T. But due to pragmatic sampling we do not have ...