Inverse Wishart Distribution
X ~ InvWishart_p(ν, Ψ)
Random-Matrix / Conjugate-Prior Family • Published July 22, 2026
The standard conjugate prior for a Multivariate Normal's covariance matrix, defined directly as the matrix inverse of the already-published Wishart (exact p=1 collapse onto the already-published Inverse Gamma, confirmed numerically). Every diagonal entry is exactly Inverse-Gamma distributed regardless of the rest of the scale matrix's structure (confirmed via Kolmogorov-Smirnov test), and the posterior-conjugacy update was verified exactly to machine precision rather than only by simulation.
This reference sheet is part of an Analyze subscription.
Subscribe to read the full Inverse Wishart Distribution reference sheet, along with every other resource in the library.
See plansPrefer a saved copy?
About This Reference Sheet
The standard conjugate prior for a Multivariate Normal's covariance matrix, defined directly as the matrix inverse of the already-published Wishart (exact p=1 collapse onto the already-published Inverse Gamma, confirmed numerically). Every diagonal entry is exactly Inverse-Gamma distributed regardless of the rest of the scale matrix's structure (confirmed via Kolmogorov-Smirnov test), and the posterior-conjugacy update was verified exactly to machine precision rather than only by simulation.
Support
X a p×p symmetric positive-definite matrix
Parameters
ν > p-1 degrees of freedom, Ψ a p×p positive-definite scale matrix