Inverse matrix gamma distribution

${\displaystyle \alpha >(p-1)/2}$ shape parameter
${\displaystyle \beta >0}$ scale parameter

${\displaystyle {\boldsymbol {\Psi }}}$

${\displaystyle p\times p}$

${\displaystyle {\frac {|{\boldsymbol {\Psi }}|^{\alpha }}{\beta ^{p\alpha }\Gamma _{p}(\alpha )}}|\mathbf {X} |^{-\alpha -(p+1)/2}\exp \left(-{\frac {1}{\beta }}{\rm {tr}}\left({\boldsymbol {\Psi }}\mathbf {X} ^{-1}\right)\right)}$

• ${\displaystyle \Gamma _{p}}$ is the multivariate gamma function.