Questions tagged [measurement-error]

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

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How to fit simulated and measured data having systematic errors?

Consider a given time series of measured data and consider a simulation - consisting of a model, possibly fed with some parameters estimated a priori (not via the measured data) - which gives another ...
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Basic question about measurement errors in Design of Experiments

After reading and applying many examples of DoE I have a question that has been bugging me and haven't found an answer so far. Usually what we see in an example or publication is the design table with ...
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Accuracy of sliding window in ARIMA models

I have 245 daily stock returns with some explanatory variables. I will compare the ARIMA and ARIMAX models with some basic machine learning techniques. The training periods will be 30, 60, 90, 120 and ...
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Correct way to combine 95% confidence interval bounds returned by a fitting routine with several measurements?

I am looking for someone to just confirm / double-check something for me with regards to errors on measurements. Let's say I am trying to determine the slope of a relationship by varying one quantity ...
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What are the signs of noisy labels in a dataset?

When learning a classification model in supervised machine learning, how can we test whether the labels in the dataset are noisy or not? Is there any particular way to check it or any specific sign to ...
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Help understanding error bars based on MAD

I "inherited" an existing codebase for statistical analysis of microscopy images that I would like to translate to more modern frameworks (read Matlab -> Python). I've come across the ...
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Description of how the count of binary patches and their size is affected by noise?

In acoustics, signals can be represented as a matrix $M$ in time, frequency, and amplitude. Obviously the signal we want to describe is always superposed over other noise, $N$: One way to analyze ...
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What would be a good method to compare the results from my model to actual measurement data?

I have a complex physical model of an engine and I get certain outputs for a given set of inputs. However, these outputs are of course, not exact and deviate from the physically observed values for ...
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Question about latent variables in Co-integration Regression

I have a question about cointegration regression models as follows: Is it common to have latent variables or regressors with measurement error in the cointegrating regression model? Is it highly ...
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Including measurement precision in a bayesian linear model

I'm using Jags to fit a Bayesian linear regression to a dataset. The model is: N[i]∼N(μ[i],τ) with precision τ and mean: ...
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Accounting for errors in measurement instead of measurement error?

I have a question regarding whether or not a certain type of statistical model exists. What I need to model is an error of measurement, and not measurement error in the sense of what I've generally ...
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What loss function should I use?

With a toy neural network, I'm trying to predict a series, which has a problem. The serie is reported cases of coronavirus, but the cases are not reported the day they are detected. Part of the values ...
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Numerical integration with measurement errors: what scheme to use?

I have an unknown 'smooth' function that is sampled at some $n$ equally spaced locations $x_i$ between $0$ and $1$, with some measurement values $f(x_i)=y_i$, but each has some Gaussian uncertainty ($(...
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Explaining a Conformal Prediction (vs NonConformal)

I'm trying to understand the definition of a conformal prediction and possibly the difference with a non-conformal prediction. What I get as a general idea is that the conformal prediction will be ...
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Std error of measurement and CIs for inter-rater observations

Reliability is often reported somewhat abstractly and can be difficult to interpret (e.g., ICC = 0.9). For test-retest reliability, it can be helpful to express measurement error in the scale of the ...
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How many days should I measure a variable to get a good estimate of 'average' behavior?

I have data for individuals, spread over a number of days. My dataset is very large: it covers way more days than what is typically feasible to collect. I want to use this to create a 'benchmark' of ...
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Estimating measurement error from repeated measurements on different objects

Suppose I measure the heights of several people, repeatedly, so that I have a small number of height measurements per person. I chose height as an example to emphasize that the true value of the ...
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How do I propagate correlated errors numerically?

I'm facing an error propagation problem in fitting some experimental data. I have measured several quantities, $m_i$, and I know from theory that $\sum_{i=0}^{n} m_i = 1$. Each of the $m_i$ has its ...
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In what order should I perform Fisher's r-to-z transformation and correction for range restriction and measurement error on correlation coefficients?

I have a two part question; both parts relate to correcting/transforming raw correlation coefficients for the purpose of a meta-analysis. Confirming my understanding of ...
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Propagation of Correlated Errors

Suppose I measure three values, a, b, and c. I know independently a+b+c = 1. a, b, and c all have some measurement error; i.e. you could have a = 0.5 +/- 0.1, b = 0.3 +/- 0.05 and c = 0.2 +/- 0.05. ...
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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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Calculation of error on x intercept

I have a question regarding the calculation of the error on the x intercept. The following equation represents the error propagation equation $$\sigma_f^2 = \sum{\left(\frac{\partial f}{\partial\...
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Interpolating between poorly-defined stratification levels - modeling with very large errors-in-variables

I'm trying to estimate the mean response error associated with a measurement device (Device A) for concentration of a chemical in solution. The measurement device uses a disposable component whose ...
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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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What the main methods to test weak exogenity of covariates

Assumptions for linear regression: weak exogenity. covariates are observed without error Say that you suspect that your covariates might be suspect to measurement problems. How can you test whether ...
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Bayesian error (Toeplitz approximation of a correlation matrix dimension mismatch with class number) [closed]

I like to solve the question of part 1 of this question form Introduction to Statistical Pattern Recognition, 2nd Edition which is: Repeat Problem 7 for a two-dimensional random field of nxn. The ...
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Standard error vs error propagation

I am trying to work out the error on the x intercept of a graph and am slightly confused as to how I should go about it. Should I use the standard error on there mean or propagate the errors via the ...
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How does the RMSE work?

I am basing my understanding of the Root Mean Squared Error on this answer. From what I understand it averages the error between the target and the prediction. The root and square parts are for ...
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Random forest (or regression) when predictors are intervals

I'm trying to fit a Random Forest model where the predictors are reported as an interval rather than a point estimate. The structure of each data point is a triplet $(\bar{y_i}, x_{i1}, x_{i2})$ where ...
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Why does R refer to the distribution family as an “error distribution” in the context of generalized linear models?

I was wondering why R refers to the distribution family as an "error distribution" in the context of generalized linear models? Normally distributed errors(residuals) of a fitted model are a key ...
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81 views

Balancing measurement error with number of samples

Suppose I am doing a physical experiment and would like to measure the output (random variable). Inherently, I introduce measurement errors when sampling the random variable. There are also sampling ...
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How to calculate errorbar for a histogram created randomly?

A cubic region of space is filled with many spheres of different sizes. Perpendicular to two of the surfaces of this cube, we send some known number of random beams, some_number, based on the ''...
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Estimating the error in a bayes parameter

I have some data $y(x)$. This data is a linear combination of a signal $s(x)$ and the noise of my instrumentation $n(x)$ i.e. $y(x) = s(x) + n(x)$ This signal is generated by some parameters $\bar{\...
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Include measurement uncertainty into model evaluation

I want to build a model, that learns how to predict a continuous variable $0\leq y\leq 0$ from input data $X$. I have a training dataset with pairs of $(X_i, y_i)$ to build that model. Nothing special....
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Instrument accuracy necessary to distinguish two values

Let's say I want to know the size of some shoes, but the size isn't marked. The real size could be any of [35,36,37...50 cm], and the shoes are made so well that their real size is exactly one of ...
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linearity of a measurement device

I like to evaluate the linearity of a measurement system. In order to do so I read ISO 22514-7 as well as Breyfogle's "Implementing six sigma". However, the procedure is still unclear to me. So I'm ...
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Error bars in a population and subtracting two populations with different error bars

Suppose I want to measure a physical quantity. Let's say that $N$ trials were performed each with individual outcome $x_i,\quad i\in (1,N)$. Then obviously the outcome of the experiment would be the ...
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Can I use RMSE as a percentage of error

I'm hoping someone can verify my assumption. I am building a regression model against an outcome variable which is a percentage. After tuning, the model outputs an RMSE estimate which I've looked to ...
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comparison between two measurement devices

I have two measurement devices accelerometer A and B. The measurement is the step time of a person walking in a corridor. A is the gold standard. I want to check the validity and reliability of B. how ...
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Should one account for absolute precision producing variable number of significant digits in a dependent variable measurement? If so how?

Sometimes data for a variable are available in absolute precision, which can create different numbers of significant digits. For example, the CDC's estimates of state prevalences and incidence rates ...
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Median or mode for measurements with erroneous outliers

Background: I am working with real measurements that likely contain two sources of error, (1) measurements that were performed incorrectly, and (2) natural variability of the measured quantity and ...
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Measurement Uncertainties and LOQ values

I have a report that lists four polyaromatic hydrocarbon components as <1 ug/kg each, with a lower bound of 0.0 and an upper bound of 4 for the sum. The clients specification for the sum is 1.5 ...
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How to calculate the standard error of a proportion estimate under misclassification?

Let's take a sample of size n from an infinite population. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would have $p =...
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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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Sampling error vs. measurement error

I have a dataset involving sensor measurements (GPS trajectories). I am using this dataset to estimate aggregate statistics such as the total distance travelled and related quantities. My ...
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Negatives values when counting the generalization error upper-bound

I would like to ask about the optimal parameter that is chosen based on the minimum value of generalization error upper bound. I attached equation, where a is the training error, n is the number of ...
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Mismatched sampling rates between predictors & response plus measurement errors on categories

Background I'm unsure how to best model data from a widget manufacturing process with measurement "uncertainties" on categorical variables (relative to an ordered indexing variable) and an overall ...
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Variance of error across different samples

I am studying linear regression and may I ask does variance of error differs across different samples? Or assume to have the same value? Thank you very much.
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How do I calculate percent error when the actual data is crosses zero?

I have two sets of data with one (shown in red below) being considered correct. I'm trying to quantify the magnitude of the difference between the correct data (in red) and the comparison data (in ...
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How do you forecast a time series that is inherently uncertain?

Most time series forecasting models take in fixed (so presumably deterministic) historical values, and then output either: A point (usually mean) forecast + forecast intervals, so $\hat{Y}_{t+1} = ...

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