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# Questions tagged [covariance-matrix]

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

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### Sampling prior covariance matrices - nested sampling

I am trying to fit a multivariate Gaussian with a non-diagonal covariance matrix $\Sigma$ using nested sampling. Usually, in other Bayesian analyses, we would use a Inverse Wishart or LKJ prior on ...
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### What is the quantile covariance?

Suppose that $X$ is a p-dimensional random vector and $Y$ is a random scalar. Then, Dodge and Whittaker (2009) indicate that the covariance of these two variables can be formulated as a minimization ...
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### How to calculate individual covariances and residual covariances in a multivariate mixed model

I need enlightenment in calculating individual covariances and residual covariances in a multivariate mixed model. I'm going to use the dataset 'Owls', present in the glmmTMB package to replicate ...
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### MSE for the kernel-based HAC long-run covariance matrix itself (in the Frobenius norm sense)

Consider the stationary multivariate time series $X_1, \ldots, X_T$ and the HAC-consistent long-run covariance matrix estimator \hat{\Gamma} = \hat{\Gamma}_0 + \sum_{l=1}^{T-1} K\left(\frac{l}{h_T}\...
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### convergence and efficiency of mcmc chains and estimation of covariance matrix

I am doing some bayesian analysis and exploring posterior distribution with mcmc method. I would like some clarification with estimating the covariance matrix. I have a model with 6 parameters. ...
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### Geometric interpretation of Cholesky Decomposition

I understand that a square matrix, say $A$, can be thought of as a linear transformation within the same space. I could be as simple as basis change or some other transformation. In this way of ...
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### How to show that $X = LY$ where $Y\sim N(0,I)$?

Let $X\sim MVN(0,\Sigma)$ denote a random vector having the multivariate normal distribution with mean $0$ and covariance matrix $\Sigma$. Suppose we want to sample from $X\sim MVN(0,\Sigma)$. ...
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### Inverse Covariance Matrix of a Gaussian Distribution: Relationship of Precision Matrix and Information Matrix

In the book "Probabilistic Robotics" (Thrun et al.), chapter 3.5.1 states that The canonical parameterization of a multivariate Gaussian is given by a matrix $\Omega$ and a vector $\xi$. The ...
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### Doubt about proof of positive semi-definite matrix implies covariance matrix

I have a doubt about the proof of the fact that a positive semi-definite matrix is a covariance matrix. The professor do the following proof: Let $\Sigma$ be a positive semi-definite $p \times p$ ...
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### What are the differences between HC estimators and their small sample properties?

I am currently using R to run regression with the following code: ...
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### Variance explained by a set of variables (dimensionality reduction) [closed]

I am interested in estimating the amount of variance that can be accounted for by a set of variables. After reading this previous post where a similar question is answered but for only one variable: ...
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### data simulation from given covariance matrix from a regression model

I have a set of data. I ran a linear model fit to the data, let's just say to a general form: $af_1(x)+bf_2(x)+cf_3(x)+df_4(x)+e$ where $a,b,c,d,e$ are the fitted parameters. I am able to get the ...
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### Correct error estimation for linear fit

This may be a simple problem, but I want to be thorough in setting up my problem as I'd like to know why I should proceed in one of two ways (or another if someone thinks it is suitable), so please ...
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### Is the first principal component is the one with the largest eigenvalue and how to convert it to explained variance?

In PCA, after we calculate the eigenvalues of each variable, we need to get the explained variance, I read an article which suggests: ...
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### What is a good measure of the similarity of 6 different time series?

Essentially, I have 6 different data time series that were each generated first using an industry standard methodology (call it method m.A) and then again using my technique (call it method m.B). ...
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### Multiplying by vectors to assess covariance is zero

I want to prove the following but am unsure how. Show that if: For all fixed vectors $c$, $Cov(X,c'Yc) = 0$ Where $X$ and $Y$ are matrices of random variables, then it must be true that: \$Cov(X,Y)=...