Given scale matrix Phi and degrees of freedom nu,
rmirror_wishart will sample from the mirror-Wishart distribution.
rmirror_wishart(nu, Phi)An integer. The degrees of freedom in the mirror-Wishart.
A matrix. The scale matrix of the mirror-Wishart.
A matrix drawn from the mirror-Wishart distribution with nu
degrees of freedom and scale matrix Phi.
\(S\) is mirror-Wishart(\(\nu,\Phi\)) if $$S = UV'VU',$$ where \(VV'\) is the lower triangular Cholesky decomposition of a Wishart(\(\nu,I\))-distributed random matrix and \(UU'\) is the upper triangular Cholesky decomposition of \(\Phi\). That is, \(V\) is lower triangular and \(U\) is upper triangular. For details on its applications, see Gerard and Hoff (2015).
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49. https://doi.org/10.1016/j.jmva.2015.01.020 http://arxiv.org/pdf/1408.0424.pdf