Efficiently generating inverse-Wishart matrices and their Cholesky factors

This paper presents a new algorithm for generating random inverse-Wishart matrices that directly generates the Cholesky factor of the matrix without computing the factorization. Whenever parameterized in terms of a precision matrix $\mathrm{\Omega }={\mathrm{\Sigma }}^{-1}$, or its Cholesky factor, instead of a covariance matrix $\mathrm{\Sigma }$, the new algorithm is more efficient than the current standard algorithm.