Linked Questions
89 questions linked to/from What is the intuition behind conditional Gaussian distributions?
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Multivariate measures of variance or spread: What is the geometric intuition or citations behind these metrics?
This question is a follow-up to: Measures of multidimensional spread or variance
I am interested in getting a multivariate measure of total variance in numeric data. Imagine we have a covariance ...
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PCA returns the same pair of principal axes for completely different 2D datasets [duplicate]
I noticed a (seemingly) weird behavior while using sklearn's PCA on 2D standardized datasets: I kept getting the same principal axes: $\pm\left(\begin{gathered}\sqrt{0.5}\\
\sqrt{0.5}
\end{gathered}
\...
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How Difficult is it to Determine the Conditional Distribution of a Non-Normal Distribution?
I have the following question about How to Determine the Conditional Distribution of a Non-Normal Distribution.
When dealing with the Multivariate Normal Distribution, there is well-established theory ...
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How to relate a covariance matrix to the generated length and angle of a elliptical distribution?
I am trying to generate a plot of points randomly sampled from a 2D elliptical distribution. I want to control the length and orientation of the ellipse this random sample creates. It seems like ...
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Interpretation of the elements of the error matrix as inverse of hessian matrix [duplicate]
In a report I am reading at work, the error matrix is calculated as the inverse of the hessian matrix and used to calculate the error ellipse angle and axes with a not theoretically correct formula.
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Intuition for correlation of N≥3 dimensional Normal distribution
What is an intuitive way to think about the covariance matrix in an N≥3 dimensional Normal distribution?
In two dimensions the covariance matrix can be visualized by plotting a region of constant ...
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Conditional expectation of two correlated RVs
$X$ and $Y$ are two correlated random variables. I am trying to estimate $E(X\mid Y)$ given $E(X)$, $E(Y)$, $\rho(X,Y)$, $\sigma(X)$ and $\sigma(Y)$. Could someone point me how to go about it. What if ...
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PCA reflections
One way of viewing PCA is a reflection and rotation of the original coordinates, while keeping the points pairwise fixed.
For exposition purposes, take a data set in two dimensions with x and y ...
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Proof that $RSS=n*\sigma_{Y}^{2}*(1-r^2)$
I have given the function for a regression $Y_i=\beta_0+\beta_1x_1+\epsilon_i$ and I'm asked to show a proof that $RSS=n\sigma_Y^2(1-r^2)$ given $r=\frac{Cov(X,Y)}{\sigma_X\sigma_Y}$, but I don't see ...
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How to derive correlation using regression without empirical proof?
I just finished learning MLE, Regression, Covariance and now in to Correlation.I want to transform logically from Regression to Correlation using Covariance.
Regression:
A simple regression model ...
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Draw scatter diagram from normal distribution
I'm currently revising for an exam and I don't understand one of the questions. Given are the following expectation / mean vectors and covariance matrices:
A) $\mu_1 = \begin{pmatrix}0 \\ 0 \end{...
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Making sense out of the standard error formula
When speaking about regression,
Why is the $SE_y = SD_y\sqrt{1-r^2}$ ?
$r$ is the correlation coefficient .
I can't really see it.
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How do I calculate the true value of the residual variance?
I have to generate a sample $(X_i,Y_i,W_i), i=1,...,1000$ from a trivariate Normal distribution with mean $(0,1,2)$ and covariance matrix $\begin{bmatrix}1 & 1 & 1.7\\& 2 & 1.5\\ & ...
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What does Nassim Taleb mean by 'half point' correlation?
Last year, Nassim Taleb posted this on Twitter:
For a correlation number between X and Y, what is the "half point" correlation between 0 and 1, that is, the correlation for which you have ...
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Completing the square and marginalizing a multivariate Gaussian [closed]
Edit: This question has been closed for being unrelated although I see similar questions posted here with the same objective, yet not with enough detailed answers or not exactly what I am looking for (...
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