Inverse-Wishart distribution ($I{W}_p(\nu ,R)$)

For positive-definite $R$ and $\nu >p-1$, if $W\sim W_p(\nu ,R^{-1})$ has the Wishart distribution, then $W^{-1}$ has the Inverse-Wishart distribution. For $\nu >p+1$, its expected value is $R/(\nu -p-1)$; below this threshold the matrix mean does not exist. It commonly models a covariance matrix, but couples the prior behavior of variances and correlations.