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.

翻译：Gaussian (MGIG) 通用反向分布矩阵样本是各种统计模型的Markov 链子 Monte Carlo(MCMC) 算法中所要求的,然而,MGIG分布的有效取样办法尚未充分开发。我们在此提议根据Choleski分解法,为MGI分布采用新的封存Gibs取样器。我们通过模拟研究和数据分析,表明拟议Gibs采样器的计算效率。我们通过模拟研究和数据分析,表明拟议的Gibs采样器的计算效率。