  Sampling from matrix generalized inverse Gaussian (MGIG) distributions is
required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of
statistical models. However, an efficient sampling scheme for the MGIG
distributions has not been fully developed. We here propose a novel blocked
Gibbs sampler for the MGIG distributions, based on the Choleski decomposition.
We show that the full conditionals of the diagonal and unit lower-triangular
entries are univariate generalized inverse Gaussian and multivariate normal
distributions, respectively. Several variants of the Metropolis-Hastings
algorithm can also be considered for this problem, but we mathematically prove
that the average acceptance rates become extremely low in particular scenarios.
We demonstrate the computational efficiency of the proposed Gibbs sampler
through simulation studies and data analysis.
