# Questions tagged [wishart-distribution]

The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.

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### Sample covariance of non-independent Gaussian vectors

Problem definition Consider the following dataset \begin{equation*} \{y_j=m+v_j\}_{j=1}^N \end{equation*} of bivariate Gaussian vectors, where \begin{equation*} m\sim\mathcal{N}(\hat{m}, P_m) \qquad ...
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### Marginal Distribution of Matrix Normal with Two Inverse Wisharts

Say I have a Matrix-Normal distribution and two Inverse Wishart Distributions $$X \sim MN_{p\times n}(0, \Sigma, \Omega)$$ $$\Sigma \sim IW(a, A)$$ $$\Omega \sim IW(b, B)$$ where $a$ and $b$ are ...
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### Appropriate Distribution for Diagonal Covariance Matrices

Let's say I have a model like: \begin{align} X\mid\mu,\Sigma_X &\sim \mathcal{N}(\mu,\Sigma_X)\\ \mu\mid m, \Sigma_\mu &\sim \mathcal{N}(m,\Sigma_\mu) \\ \Sigma_X\mid \Psi, c &\sim \...
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### Intuitive explanation of Inverse Wishart prior for covariance estimation

I am trying to understand what is going on in the use of an Inverse Wishart prior for (Gaussian) covariance, and what is the motivation for it. I am seeing this posed as a solution for when the ...
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The subject is about the sample mean and the sample covariance estimators and their respective confidence regions for the estimated parameters. Suppose that $n$ samples are taken from a $p$-variate ...