# Tagged Questions

A $k\times k$ matrix of covariances between all pairs of $k$ random variables. It is also called variance-covariance matrix or simply variance matrix.

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### A measure of “variance” from the covariance matrix?

If the data is 1d, the variance shows the extent to which the data are different from each other. If the data is multi-dimensional, we'll get a covariance matrix. Is there a measure that gives a ...
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### The covariance matrix is not positive definite in a classification task in Matlab

I am trying to perform a simple classification task in Matlab. I have an NxM matrix F with rows representing the samples and column representing the features (that is my training set). This is fed to ...
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### Recursive least squares with forgetting factor - parameter covariance

The recursive least-squares algorithm equipped with forgetting factor is summarized as \begin{array}{l} \hat \theta \left( t \right) = \hat \theta \left( {t - 1} \right) + L\left( t \right)\left[ {y\...
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### Whitening transform for the case of two stochastic processes

The classic whitening transform allows us to find a linear transformation for a given random process X, yielding a new process Xw with a unity Covariance matrix. Given an extended problem with two ...
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### Why are symmetric positive definite (SPD) matrices so important?

I know the definition of symmetric positive definite (SPD) matrix, but want to understand more. Why are they so important, intuitively? Here is what I know. What else? For a given data, Co-...
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### How to apply different values for input noises in GPML toolbox?

As you probably know, GPML toolbox accepts only one value for noise in both white noise covariance function and likelihood. Actually in my case, each input data has its own value for noise (16 ...
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### Algorithm for mixed-effects models with 100 random effects

I am wondering if there is any algorithm can estimate a mixed-effects model with 100 random effects, i.e., the covariance matrix $\boldsymbol D$ for random effects is 100$\times$100. I tried the ...
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### Is autocorrelation not worth addressing with small N?

Consider a simple regression context in which there is a small set of response values, $Y$, and corresponding dates, $X$. (For simplicity, we can assume the dates are equally spaced.) We would like ...
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### How to propagate scaling uncertainties into a covariance matrix?

Say I have a covariance matrix $C$ given in a certain unit (say, kg^2), corresponding to measurements made in this unit. All measurements are done in this unit. Say, further, that I want to convert ...
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### How do I calculate (or approximate) the covariance matrix of a multivariate Gaussian distribution with only the variances of the components?

With the constraint that all components sum to a given specific real number; The Mean vector is also known; No sample available; correlations between any two of the components is unknown.
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### Covariance Matrix for Time Series

I'm trying to investigate how events affect the stock market through econo-physics and I came across a paper that uses the co-variance matrix. What I don't understand is how such a matrix can be ...
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### Estimating correlation(covariance) matrix when fitting a copula using R copula package [migrated]

I have a question about the R package copula. When using fitCopula to fit a copula to data, ...
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### Are a sum and a product of two covariance matrices also a covariance matrix?

Suppose I have covariance matrices $X$ and $Y$. Which of these options are then also covariance matrices? $X+Y$ $X^2$ $XY$ I have a bit of trouble understanding what exactly is needed for ...
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### Covariance between non symmetrical matrices with a unidirectional composition

I am trying to explain variation in why some researchers go to certain places and not others by analyzing how many articles scientists from one publish about another location. My matrix is ...
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### Covariance Matrix and Correlation Matrix - Singularity

If a covariance matrix is non-singular, does this implies that correlation matrix is also non-singular. My guess is it depends on mean vector in $K_{X} = R_{X} - m_X.{m_X}^H$ Not sure though.
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### Common covariance matrix in linear discriminant analysis

Say I want to perform LDA classification involving three classes with within-class covariance matrices $$\hat{\Sigma}_1 \,, \hat{\Sigma}_2 \, , \hat{\Sigma}_3$$ and that these matrices are calculated ...