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The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.
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Transformation of Inverse Wishart
Let $\Sigma$ be an $p\times p$ dimensional covariance matrix that is distributed Inverse Wishart with degrees of freedom $\nu$ and Prior scale matrix $\Psi$ such that we write $\Sigma \sim W^{-1}(\nu, …
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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 d …