Suppose we have the variance matrix, which is Wishart distributed:
$\begin{pmatrix} s_1 & c_{12} & c_{13} & c_{14}\\ c_{21} & s_2 & c_{23} & c_{24}\\ c_{31} & c_{32} & s_3 & c_{34}\\ c_{41} & c_{42} & c_{43} & s_4 \end{pmatrix}$
What I am trying to define is the marginal distribution of its right upper part: $\begin{pmatrix} c_{13} & c_{14}\\ c_{23} & c_{24}\\ \end{pmatrix}$
I know that it is possible to find the marginal distribution of off-diagonal elements of 2x2 Wishart matrix by using variance-gamma distribution:
$f_{c_{ij}} = \dfrac{|c_{ij}|^\tfrac{n-1}{2}}{\Gamma(\dfrac{n}{2}) \sqrt{2^{n-1} \pi (1-\rho^2) (\sigma_i \sigma_j)^{n+1}}} K_{\tfrac{n-1}{2}} (\dfrac{|c_{ij}|}{\sigma_i \sigma_j (1-\rho^2)}) \text{exp} (\dfrac{\rho c_{ij}} {\sigma_i \sigma_j (1-rho^2)})$,
where $K$ is the modified Bessel function of the second kind, $c_{ij}$ - the off-diagonal element, $\sigma_i$ and $\sigma_j$ - diagonal elements.
Is it possible to somehow modify this definition for 4x4 case? Or is it valid to apply it directly to the case of 2x2 submatrix I am trying to consider?