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

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21 views

Error on histogram computed on autocorrelated time series

I am struggling to find an answer to this quite basic question. When computing a histogram on a time series which has some correlations (i.e. measurements are not independant), how to estimate the ...
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1answer
17 views

Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
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108 views

Bayesian modelling, measurement error & carrying-over posterior distributions

I have a (fairly convoluted, but well-inentioned) model in my head, and am trying to figure out if it's possible to code (I am currently getting to grips with R2WinBUGS). The final model is basically ...
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24 views

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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0answers
42 views

How to measure error in linear regression?

Suppose I have $X, Y =$ {$(x^{(1)}, y^{(1)}); (x^{(2)}, y^{(2)}); ...; (x^{(m)}, y^{(m)})$} examples with: $x^{(i)} \in \Re^n$: for $i$ $\in$ [1;m], $x^{(i)}$ = {$x_1^{(i)}, x_2^{(i)}, ..., ...
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1answer
90 views

Is it true that $E[Y|W]=E[Y|E(X|W)]$, given that $W$ is $X$ measured with error

In Carroll's 2006 book "Measurement Error in Nonlinear Models", and on p38 it is stated without proof that: [One can] estimate the regression of $Y$ on $(Z, X)$ and then to substitute into this ...
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4answers
53 views

Poor sample measurement and the Central Limit Theorem

I have a fairly basic question about the Central Limit Theorem. I understand it in principle, but I like to know specifically what happens when there is poor measurement on the samples. Say for ...
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22 views

Testing interactions with non-normal ordinal data

I am testing a hypothesis in which my scale DV (PSS) is predicted by an interaction between an Ordinal DV and a scale IV. The ordinal IV is TF (Total Freq) The scale IV is and PQM (Practice ...
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1answer
6 views

Measuring dispersion of data points

I have a number of data points (which can be small) with measurement error bars. I assume the intrinsic values are drawn from some sort of normal distribution. What is the most robust method for ...
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0answers
14 views

Error propagation and Standard Deviation

I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now. Lets assume I'm trying to find the focal length of a concave lens. Using a mockup ...
0
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0answers
36 views

Making Predictions in an Error in Variables Model

Say I have estimated some parameters $\hat{\beta}$ between input $x$ and output $y$, according to a generalised linear model $y=x^T \beta$, by using the Least Squares method. I can then easily make ...
0
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1answer
44 views

Question on error minimization, bias and variance

I have been using Matlab to approximate a density function using histograms with a fixed number of bins. The histogram is on the interval $[-10,10]$ with a bin size of $0.05$. This makes 400 bins. ...
2
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28 views

Calculate the Hamming Distance between the two same datasets

How to Calculate the Hamming Distance between two datasets of same points?Both the data sets look exactly the same. http://postimg.org/image/u11qnsolh/ There are two datasets of same number of ...
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1answer
81 views

The effect of covariate measurement error on coefficients in regression with dummy variables

I am trying to understand if I should be more concerned with covariate measurement error in linear models including dummy variables, than with all continuous predictors. Say I have a simple linear ...
1
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1answer
55 views

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 ...
0
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0answers
16 views

MSE of training set and validation set for linear regression

The wikipedia article on cross validation http://en.wikipedia.org/wiki/Cross-validation_(statistics) makes the claim that "under mild assumptions that the expected value of the MSE for the training ...
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0answers
22 views

How to fit quantized data

I have some measurements which were quantized during measuring. Now I want to get the overall change during a period of time, e.g. 15 minutes. Because of quantization however, the same value is ...
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1answer
41 views
0
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0answers
23 views

Is it okay to use relative error on a set of measurements rather than an absolute error?

As far as I've learned, if you have a set of measurements and the differences between the average of those measurements and the individual measurements aren't always smaller than the absolute error of ...
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0answers
17 views

Interaction model with measurement error without replicate measurements

I am currently working on a simple OLS model with two independent variables and one dependent variable: \begin{equation} \ Y_i = \beta_0 + \beta_1 X_i + \beta_2 S_i + \beta_3 X_iZ_i \end{equation} ...
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0answers
31 views

Propogation of error in a matrix inversion

I'm trying to find the deterministic error bounds for some parameters calculated through distance geometry. The equation can be simplified to the following form: $ \left[\begin{matrix} x_1 \\ x_2 \\ ...
2
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0answers
18 views

How do you report percent error with limited precision?

Let's say you have an experimental data point with limited precision, such as 0.67 ± 0.1, and a known actual value such as 0.72. What is the standard way to report the percent error in this case, ...
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0answers
17 views

How should I handle measurement error in logistic/probit regression and what are its effects?

I am concerned with the problem where dependent discrete variable $R$ is to be modelled by continuous predictor $X^*$, which is subject to measurement error $u$ of the form $$X^*=X+u$$ ($X$ being the ...
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0answers
39 views

Accounting for measurement bias using a histogram or violin plot and numerical data in R

The Problem I have a gardener whose job it is to measure trees in meters using a measuring stick. She measures the heights of 1,000 trees. I plot these measurements on a violin plot in R. I am ...
3
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1answer
56 views

non-classical measurement error in a binary outcome model

I have a binary outcome model that I am estimating with a probit, so $$\Pr(Y=1\vert x,z)=\Phi(\alpha +\beta\cdot x^* + z'\gamma)$$ I am interested in the marginal effect of $x^*$ on $\Pr(Y=1\vert ...
9
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1answer
282 views

Additive Error or Multiplicative Error?

I'm relatively new to statistics and would appreciate help understanding this better. In my field there is a commonly used model of the form: $$P_t = P_o(V_t)^\alpha$$ When people fit the model to ...
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1answer
21 views

IV or latent factor to process multiple measures?

I have several measures on different memory tests. I consider these measures may actually measure different aspects of memory functioning and every measure contains a measurement error. I am thinking ...
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36 views

Robust Measures for Forecast Accuracy

I am doing a forecast using robust exponential smoothing methods and to determine / measure the forecast accuracy I want to use robust measurements as well. As I am not really familiar with robust ...
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0answers
66 views

Machine learning/random forests with noisy response data

Machine learning techniques like random forests seem to assume that the responses in the training set are known perfectly. Specifically for regression applications, it seems one needs to account for ...
2
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1answer
76 views

Accounting for unknown error in multiple regression?

I have a very naive question about multiple regression and errors...one that isn't addressed here already (Choosing a robust estimator to account for measurement error in dependent variable) I would ...
2
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0answers
29 views

does the area under the curve (AUC) has some interpretation? [duplicate]

I know that the ROC curve plots true positives vs false positives, but does it have any other interpretation, or is it just an arbitrary performance measure? Also, in the case of very unbalanced ...
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0answers
19 views

Need to determine stability of a measure over subsets

I have a measure that takes a set of data and spits out a value. I want to determine the stability of this measure in terms of the size of the dataset. I.e, I want to understand how the returns (for ...
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0answers
38 views

Measurament error from semivariogram

I am looking at a model to determine the measurement error for a set of measurements of a spatially correlated phenomenon (sea surface temperature measurements) using a semivariogram technique. For ...
2
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0answers
42 views

Fast Estimation of Random Effects with Measurement Error

Let $Y_{i}$~$Normal( Z_{i} , \sigma_{i}^{2})$ and $Z_{i}$~$Normal(0,\tau^{2})$, where $Y_{i}$ is a measurement, $\sigma_{i}$ is known measurement error, $Z_{i}$ is the unknown latent variable I want ...
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38 views

Combining separate accuracy and precision calculations for characterizing the performance of a device

I have created a device that produces chemical mixtures of user-defined concentrations and am now working on characterizing the performance of this device. In order to do this, I created 3 replicates ...
2
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1answer
35 views

Interpreting a logarithmic difference as an error

This is a fairly simple question but I can't figure out which one is the correct approach. In astronomy it is usual to report age values via their base 10 logarithms instead of the actual value. So a ...
4
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1answer
51 views

Intuition for what happens to the standard deviation after plugging a normal variable into a function

Let's say I have a normal variable $X$. I feed $X$ into some function, which applies varies mathematical operations to it - for instance, addition, subtraction, multiplication, division, $x^r$, $e^x$, ...
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17 views

How to separate model errors from measurement errors?

I've got data measured with errors that have known measured_RMS. I am testing a model that has model_RMS differences between model prediction and measured data. What would be a reasonable estimate of ...
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0answers
12 views

Using confidence level for error evaluation

I want to evaluate performances of a forecasting system. I have some samples of the whole population. But what i actually have is the mean value of the sample and the forecast for the mean of the ...
2
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1answer
60 views

Difference in 2 groups when group assignment is not certain

Suppose you have two groups and you want to see whether these two groups differ in regards to some variable. This sounds like a basic t-test or perhaps non-parametric Wilcoxon rank sum test. Suppose ...
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0answers
6 views

How to properly calculate error in a decompressed column of floating point numbers?

I have a series of floating point numbers, compress it with some lossy compression algorithm and decompress it. I want to be able to calculate the error produced by this procedure. What I've done is ...
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26 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
0
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1answer
60 views

What is Median Error Distance and how to calucalte it

How to calculate Median Error Distance? I'm looking at "Schulz A. et al. A Multi-Indicator Approach for Geolocalization of Tweets". They are calculating Median Error Distance. But how they are do ...
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0answers
18 views

Distribution of average and median of a random variable [duplicate]

Suppose I have some random variable, which is defined by certain distribution (e.g. triangle or normal or some other). Suppose I do $N$ independent measurements on this random variable and then ...
2
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0answers
35 views

Measurement Error in Dynamic Linear Model

I have fitted a dlm model as follow: ...
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0answers
19 views

Tools for determining final error with mixture of correlated and independent sources of error

Preface: Not looking for an answer, but rather seeking an approach or set of approaches to deal with a complicated problem. Brief version: I have a single, analytical set of 3 equations with 8 ...
0
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1answer
17 views

error summary metric

I am working on trying to get a summary metric that summarizes the results of four models (M1:M5) and preferably ranges from zero to one, with one being the best model and zero being the worst model. ...
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0answers
113 views

Estimating the uncertainty of a bias and a scatter

I have one single set of observational data. Assuming I know the right answer for one property of this data set and then I use one tool to measure this quantity. To get an estimate of the amount of ...
7
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1answer
74 views

Selecting priors based on measurement error

How do you calculate the appropriate prior if you have the measurement error of an instrument? This paragraph is from Cressie's book "Statistics for Spatio-Temporal Data": It is often the case ...
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0answers
16 views

How do you scale percentage intervals based on absolute size?

If you were told the travel time from A to B is 5 minutes, you wouldn't mind if it took between 0 and 10 minutes. So happy within 100% of 5 minutes. If the trip took 5 hours (360min), you wouldn't ...