  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 $\Omega=\Sigma^{-1}$, or its Cholesky factor, instead of a covariance
matrix $\Sigma$, the new algorithm is more efficient than the current standard
algorithm.
