Inverse-Wishart Distribution

Density

The probability density function of the inverse Wishart is:

$\frac{\left|{\mathbf\Psi}\right|^{\frac{\nu}{2}}}{2^{\frac{\nu p}{2}}\Gamma_p(\frac{\nu}{2})} \left|\mathbf{X}\right|^{-\frac{\nu+p+1}{2}}e^{-\frac{1}{2}\operatorname{tr}({\mathbf\Psi}\mathbf{X}^{-1})}$

where and are positive definite matrices, and Γ_p(·) is the multivariate gamma function.

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Inverse-Wishart Distribution - Density