Questions tagged [wishart]

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

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Expected value of the log-determinant of a Wishart matrix

Let $\Lambda \sim \mathcal W_D(\nu, \Psi)$, i.e. distributed according to a $D \times D$ dimensional Wishart distribution with mean $\nu \Psi$ and degrees of freedom $\nu$. I would like an expression ...
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Hyperprior distributions for the parameters (scale matrix and degrees of freedom) of a wishart prior to an inverse covariance matrix

I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R. Instead of specifying a scale matrix and degrees ...
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Suppose $S$ is distributed as a Wishart matrix with $n$ degrees of freedom and scale matrix $\Sigma$, and let $\vec{a}$ be a fixed vector. It is well known that $\vec{a}^{\top}S\vec{a}$ is equal to $\... 1answer 319 views What is the correct form of Metropolis Hasting step in scaled Inverse Wishart prior for covariance matrix? I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed ... 1answer 3k views How to sample from a Wishart distribution? From Wikipedia, we know that$n$, the degrees of freedom, should be larger than$p-1$where$p$is the dimension of the scale matrix. Also, from the bottom part of the same article, we see "Bartlett ... 1answer 79 views Integrate out (covariance) matrix in Normal-Wishart distribution In Gelman's Bayesian Data Analysis Chapter 3.6, he introduces the multivariate normal with unknown mean and variance, with the priors$\Sigma\sim \text{Inv-Wishart}_{\nu_0}(\Lambda_0^{-1})\mu\...
The Inverse-Wishart wikipedia article states that $X \sim \operatorname{Wish}^{-1}(\Psi,\nu)$ if $X^{-1} \sim \operatorname{Wish}(\Psi^{-1},\nu),$ where $\Psi$ and $X$ are $p\times p$. The mean ...
Expected value of $E[S_{ki}S_{kj}]$ in wishart dist
Some details: We know that the Wishart distribution with $\nu$ degrees of freedom and positive definite $p \times p$ scale matrix $V$, $\mathcal{W}_p(\nu,V)$, has the pdf \$p(S|V,\nu) = \frac{|S|^{(\...