# Questions tagged [wishart]

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

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### Property of Wishart distribution

I am solving the next exercise about a property of a Wishart Distribution: $$M_1\sim W_p(\Sigma,n_1)$$ $$M_2\sim W_p(\Sigma,n_2)$$ are independent, then $M_1+M_2\sim W_p(\Sigma,n_1+n_2)$ I have ...
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### Result for covariance between elements of the sample covariance matrix

Given data matrix $X_{n,p}$ where $n$ is the sample size, $p$ is the dimension, the sample covariance is $$\hat{\Sigma}=\frac{1}{n-1}X^\top X=\{\hat{\sigma}_{ij}\}_{1\le i,j\le p}$$ Is there any ...
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### What is the correct form of Metropolis Hasting step in scaled Inverse Wishart prior for covariance matrix?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed ...
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### expectation associated with Wishart distribution

Suppose that $W$ follows the Wishart distribution with parameter $\Sigma$ and d.f. $n$. Then, I would like to know the result of the following expectations. $E[tr(WAWB)tr(WC)]$ $E[tr(WAWB)tr(WCWD)]$...
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### Informative prior for Normal-Inverse Wishart distribution

In Bayesian analysis we use the Normal-Inverse Wishart distribution for the parameters of multivariate models these prior distributions have some hyperparameters. So how do we find the values of ...
Is the following integral solvable? $$P(X) = \int^{\infty}_{-\infty} \int^{\infty}_{-\infty} P(X|\mu,K)P(\mu|K)P(K) d\mu dK$$ with P(K) = \frac{|K| ^{(v-d-1)/2}}{2^{vd/2}|V|^{v/2}\Gamma_d|\frac{...