Questions tagged [error]

The error of an estimate or prediction is its deviation from the true value, which may be unobservable (e.g., regression parameters), or observable (e.g., future realizations). Use the [error-message] tag to ask about software errors.

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8 views

Systematic Error Propagation with a Linear Fit

I am doing a Physics experiment in Atomic Spectroscopy. I am trying to find the wavelengths of certain spectral lines. The wavelength readout on our monochromator is not correct, so we must calibrate ...
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3answers
53 views

Assumption that $E(u) = 0$

I have been thinking about this question for a while: We assume that $E[u_i] = 0$. What are the implications for the OLS estimator if this assumption is not valid? Explain why this may or not be the ...
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How to interpret expectation of one specific observation of $u_i$, eg. $E[u_1|X]$?

I'm a bit hung up on how to interpret the expectation of a single observation of the error term... especially in the context of the zero-conditional mean assumption. If the true population model is ...
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21 views

How do I propagate asymmetric error/confidence intervals? [closed]

Assume that I have two measurements with asymmetric error, $X^a_b$ and $Y^c_d$, and I want to find $Z^e_f = X^a_b + Y^c_d$. How do I find Z? The type of answer I'm looking for is of the form : $e = ...
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6 views

Comparing Modelled/sampled distance time graphs

I am comparing the journey times of modelled vs observed of vehicles along a set of roads. Usually this would be done visually but obviously the line will always be biased to appear to be correlated ...
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7 views

Error distribution

I am working on a urgent message classification problem using CRF(Conditional Random Fields). I have obtained a confusion matrix from the model and now I want to check the error distribution i.e. ...
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0answers
16 views

Dealing with upper limits when fitting data

Let's assume that I have a set of data composed by two measurements, X and Y (plus respective errors), and I am interested in studying their linear correlation, i.e., finding a linear best-fit Y = a*X ...
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1answer
27 views

How to quantify measurement error

I would like to determine the measurement inaccuracy one of our laboratory machines in different conditions: Let's say for simplicity's sake it is a b/w digital camera with 1024x768 pixels (786,432px)...
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6 views

What does error rate means in a random forest model?

I have found an error rate of 31.77% for my random forest model. I have grown 10,000 trees. I don't understand what does an error rate means in a random forest. Thank you for your help :)
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2answers
44 views

What is the difference between an RMSE and RMSLE (logarithmic error)?

RMSE vs RMSLE Root Mean Squared Error (RMSE) and Root Mean Squared Logarithmic Error (RMSLE) both are the techniques to find out the difference between the values predicted by the machine learning ...
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1answer
33 views

Can't .632+ rule be computed for any kind of outcome and prediction score?

It seems that the R packages I found around for computing the .632+ estimation of prediction error work only with categorical outcomes. Why is that? Looking at the formulas in Efron 1997 paper it ...
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4 views

Error analysis in rate of counts and symmetric feature of a detector

I'm going to conduct an experiment. In the experiment, I have a smoke detector. I want to find how symmetric is the detector in terms of rate of detecting particles. Here is the data in three times ...
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20 views

error vs. deviation vs. difference

What exactly is the difference between the way these terms are used in statistics? As far as I can tell they mean the same thing mathematically, but it's unclear to me whether and how usage depends ...
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1answer
68 views

Variance of the binomial distribution

Suppose you use MC events to determine a selection efficiency. Where the efficiency is defined by: $$\epsilon = \frac{m}{n}$$ n is the number of fixed number of trials m is the accepted numbers ...
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50 views

Finding the in-sample error rate of a discriminant model with multiple predictors

I have run in R a linear discriminant model and a quadratic discriminant model. Here's are my equations : How can I find the overall in-sample error rate of my linear discriminant model in R? How ...
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25 views

Bootstrapping across residuals for heteroscedastic data

I have a highly heteroscedastic 2d dataset (x,y) where both x and y cover about 3 orders of magnitude; therefore, although the % error is roughly constant and normally distributed across x, the ...
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10 views

How to choose a threshold for error measurment in a given dataset

I am working with a given dataset of measurements, each one with an associated error. I want to establish a threshold for this error, to maximize the data quality. Is there an statistical approach on ...
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38 views

Find Error in the vertex of a fitted parabola

I have a set of data (a Cross-Correlation function) to which I've adjusted a parabola (using lmfit python package ), from the fit I got the values of the parameters and their error: (Model): $f(x; a, ...
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27 views

How to fix 'Error() model is singular' when running a mixed ANOVA in R

This is my data set I am trying to run a mixed ANOVA on in R. Subject Substrate Biomass Pb ...
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1answer
36 views

MAPE and SMAPE shift invariance (bias)

MAPE (Mean Absolute Percentage Error) and SMAPE (Symmetric Mean Absolute Percentage Error) both are sensitive when the TRUE ...
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23 views

Bounded loss function whose minimizer is the mean

Let $$ y = \operatorname*{argmin}_\hat{x} \operatorname*{E}_x L(|\hat{x} - x|) $$ where $L$ is a loss function. As noted here, if $f(s) = s^p$ then $p \rightarrow 0$ implies $y \rightarrow$ the ...
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12 views

Mean Percentage Error on k-fold CV vs. Training Set

I'm performing a regression using a Gradient Boosting Machine. When comparing the cross-validation predictions with the true values, the Mean Percentage Error is around -6%. However, using the model ...
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1answer
30 views

Weighting the data for a fit

I have 5 data points with errors associated to them $y_i\pm dy_i$ and the corresponding $x_i$ values (which don't have uncertainties associated to them). I need to calculate the difference between the ...
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4 views

How to extract systematic errors from data

I am a bit confused about estimating the systematic error (I think it is systematic) from an experiment. Here is a (simplified) description of it. Assume that 2 groups measure the length of a cube ...
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43 views

Different reconstruction errors using different PCA algorithms

In Matlab, I perform PCA on a centered and scaled (std-scaled) data set X_cs in four ways: builtin pca using the builtin ...
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1answer
111 views

What is the relationship between estimation error, approximation error, bias, variance in machine learning?

I'm a beginner in machine learning. I was reading http://ciml.info/ 5.9 Bias/Variance Trade-off According to this book: The trade-off between estimation error and approximation error is often called ...
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1answer
65 views

AutoEncoder Reconstruction error for Anomaly Detection

I'm building a convolutional autoencoder as a means of Anomaly Detection for semiconductor machine sensor data - so every wafer processed is treated like an image (rows are time series values, columns ...
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29 views

Bayes classifier and unavoidable error

Consider the following two-class classi cation problem, where $Y = 0 \text{ or } 1$. Suppose $Y$ is a random variable satisfying$ P(Y = 0) = \frac{1}{3}$ and $P(Y = 1) = \frac{2}{3}$: Moreover, we ...
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30 views

Specification on power spectral density for population data

What is the best way to put a specification on the single-side auto-power spectral density (PSD)? We have a product for which we have a time signal. For this signal we calculate the PSD (or ...
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20 views

How is the total error equation derived?

In this video Ng said that there is a Bayes optimal error(also called irreducible error), and in this article I learned that the total error is equal to the squared bias plus the variance plus the ...
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3 views

Error Analysis For Denoising?

I have a collection of noisy audio files and their corresponding "clean" versions. I used some statistical methods like low-pass and high-pass filtering to try and remove the noise in these noisy ...
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1answer
71 views

WMAPE / WAPE for the evaluation of time series with positive and negative values

I have a time series y that has both positive and negative that I want to predict. For the prediction I normalize the values to a range between 0 and 1. If I give ...
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20 views

How do you interpret regression including log(GDP)?

I have the regression equation: Growth = B0 + B1 * log(GDP) I'm trying to understand how I would interpret this. Let's say B1 = 0.05 (se: 0.001). Would this be ...
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37 views

What is a Good Error Target

I am modeling a forecast for product categories using auto Arima in R. I'm getting MAPE of between 9-15% on average. We don't have any historical records of forecasts vs actual so I don't know how ...
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11 views

Error weighting in two point regression analysis [closed]

I have following problem: I do measurements of the formation of a product at two time points (t=0 and t=15), each in triplicates. Afterwards I calculate the mean value + the standart deviation of ...
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23 views

Estimating the Variance of the error term in Simple Linear Regression

I have the model $Y|(X=x) = \beta_0 + \beta_1 x + \epsilon $ where $Y\sim \mathcal{N}(\beta_0 + \beta_1 x,\sigma^2)$. (We omit the "$|X=x$" below for conciseness) I want to estimate the $\sigma^2 =\...
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18 views

How to calculate errors for cumulative distribution function

I have some data points of the form $(x_i,y_i,\delta y_i)$, where $y$ are counts and the error associated to each $y_i = N$ is $y_i = \sqrt{N}$. I want to create the cumulative distribution of these ...
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43 views

How to properly bin the data for a fit

I am working on a spectroscopy project in which we adjust the wavelength of a laser and get some counts on the detector from some laser-atom interactions. The data that we have is in the form: $(\...
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13 views

Quantifying error with paired measurements from multiple conditions

I have a set paired measurements (continuous values) obtained using different sample types and different methods. I.e., for each subject, I have measurements for samples A and B each on device 1 and 2 ...
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0answers
15 views

Within-subjects aov() output error term interpretation

What does it mean when the main effect of an independent variable appears twice in the output (once under Error:Pno, and once under Error: Within)? My data set (mydata) looks like this: 4 columns (...
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1answer
36 views

RMSE with and without standardizing the output variable

I have a time series data that I would like to be able to forecast. I was trying to standardize the data as my columns are all of different ranges. I have standardized the input variables, but was ...
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0answers
17 views

Errors on the mean

I have some data points from a measurement of a given quantity, and each point has an error associated to it. I want to report as the final value the mean of the measurements, but I am not sure what ...
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0answers
31 views

What is default error threshold Tensorflow? [closed]

My homework states that I am asked "to report the default error threshold used in the TensorFlow default configuration for convergence. Usually it is documented for MNIST and CIFAR-10". What's that? ...
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1answer
38 views

Dividing the MAE by the average of the values

I would like to parse the MAE (Mean Absolute Error) to a percentage value. I know there is the MAPE (Mean Absolute Percentage Error), however it has some drawbacks as going to infinity if one of my ...
2
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1answer
29 views

How to determine whether a validation study produces acceptable results?

I have a method developed to predict results of a signal that outputs an root mean squared error (RMSE) for each subject. Combining all 40 subjects (2 samples for each subject), I get a mean RMSE of 5....
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1answer
31 views

Fitting data with unknown noise with complicated model — can anything be done?

I have some experimental data, where due to the nature of the experiment (which I am not familiar with) the errors are not known. The data follow a rough non-linear trend but clearly are noisy as for ...
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50 views

How do I correctly estimate the size of a subpopulation using noisy observations?

To preface this question: please comment on whether my description of the problem is missing details or the problem itself is not well-posed as I'm seeing a lot of views but no activity. I am trying ...
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0answers
19 views

Comparing predictability of outcomes across leagues

From time to time I encounter newspaper articles with titles like “Unpredictable English Premier League Keeps Us Guessing”, which make claims about the difference in predictability of outcomes across ...
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0answers
16 views

Error terms (Et) of (S)ARIMA equation outisde R program

(EDITED) I used R forecast package and the best fit resulted in (1,1,2)(1,0,1) [7] with one regressor variable (X). I built the equation as follow: ...
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50 views

How can I reduce the noise of prediction graph? [duplicate]

I am trying to use LSTM to predict a time series data as you can see in the following image, the predicted graphs is very noisy: The original data is looking like this: That I normalized it like ...