Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [ellipse]

For on-topic questions involving the geometrical object ellipse, for example confidence ellipsoids. For purely mathemathical questions about ellipses, it is better to ask at math SE https://math.stackexchange.com/

Wikipedia has an article https://en.wikipedia.org/wiki/Ellipse with further information and references.

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Real meaning of confidence ellipse

Reading about the true meaning of 95% confidence ellipse, I tend to come across 2 explanations : The ellipse that contains 95% of the data Not the above, but the ellipse that explains the variance of the data. I am not sure I understand correctly…
Kenny
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Find data and confidence "ellipses" (regions?) for a bivariate median?

I'm wondering about ways to compute data and confidence ellipses around a bivariate median. For example, I can easily compute a data ellipse or a confidence ellipse for the bivariate mean of the following data (here just showing a data…
Gavin Simpson
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Proper way of estimating the covariance error ellipse in 2D

I am aware of this question but my issue is about two competing ways of obtaining the 2D covariance error ellipse in two competing answers over at StackOverflow. The first answer obtains the width and height of the ellipse as: $$w=2\times nstd\times…
Gabriel
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Confidence Interval for least squares estimator

There was a paper by Yasin-Abbasi-Yadkori https://arxiv.org/pdf/1102.2670.pdf titled Online Least Squares Estimation with Self-Normalized Processes. I am trying to give a brief context before asking my question. Let $\{x_t, y_t\}$ be data not…
rostader
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Why is a confidence ellipse based on multivariate-t tighter than one base on multivariate norm (R)

I want to draw a 95% confidence ellipse around my bivariate data. Using ggplot2::stat_ellipse() with type="t" (for a bivariate-t distribution) the confidence region is tighter than for type="norm". This is counter-intuitive, and there is very…
LBR
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Ellipse formula from points

Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)? Background: Using R Momocs library function conf_ell which returns confidence ellipse coordinates. Would be nice to…
Neil Varnas
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Using ellipses, how can I visually compare two estimated covariance matrices in the presence of sampling uncertainty?

I have with me two data matrices each of dimension n x p where n is the number of rows of observations and p = 2 is the number of variables. Each data matrix yields a covariance matrix using the standard sample covariance estimate. My aim is to…
J. Doe
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Select ellipsoid data cloud "equivalent" to a spherical data cloud

What will be your considerations when you've got to realize the intuitively plain, but meditatively manifold idea to create a data cloud which "the same as" that data cloud, only that it is not spherical in shape, like it, but is ellipsoid (or…
ttnphns
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What is the correct name for a so-called "confidence ellipse"?

We often see the terminology "confidence ellipse". This is not correct: in dimension 2, an ellipse is a curve, and the confidence region is the interior of this curve, not the curve. Similarly, in dimension 3, an ellipsoid is a surface, not a…
Stéphane Laurent
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How do I interpret the angles of two concentration ellipses?

Consider a map with two concentration ellipses like this below. The Vomit_y group is (almost?) perfectly vertical, while the Vomit_n group seems to be oriented at about 45 degrees. I understand that Vomit_y displays no correlation between Dim1 and…
Brett Reynolds
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Confidence interval of amplitude and horizontal shift

I have a linear model with sine and cosine wave as predictor. Y~$\alpha$sine(...)+$\beta$cosine(...). From the parameter estimation, I know the estimation of the coefficients are: $\hat\alpha$ = 0.65(sd = 0.15), $\hat\beta$ =0.54 (sd=0.15). The…
Huang Rui
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Question about eigenvalues and ellipses

Please consider the snippet below out of Bishop's book on PRML. According to my understanding of an ellipse, the radii are $\sqrt\lambda_{1}$ along the horizontal axis ($w_1$) and $\sqrt\lambda_{2}$ along the vertical axis ($w_2$). When looking at…
user173192
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How to estimate an ellipse's parameters from the points scattered around it?

The scatter plot shows two data series (x,y) the are placed somehow around a tilted ellipse. This is in fact the way I have drawn this example plot. Which statistics of the data sets are the most suitable to estimate back the geometrical parameters…
XavierStuvw
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How to Draw an Ellipse around a Specific Portion of a Probability Density Function

I currently have a 2D probability density function and need to draw a 2D ellipse that circumscribes 50% of the probability "mass" (if that is the right terminology). I see lots of articles on how to draw these ellipses for traditional x,y…
user7432320
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Interpretation of ellipse3d in R

I was looking at the information provided as part of the "A complete guide to 3D visualization device system in R - R software and data visualization” and was hoping that someone could provide a layman's explanation or interpretation of what the…
Dave
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