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：在马尔可夫链蒙特卡洛算法中，矩阵广义逆高斯分布的采样是多种统计模型所必需的。然而，针对矩阵广义逆高斯分布的高效采样方案尚未得到充分发展。本文基于乔列斯基分解，提出了一种新颖的分块吉布斯采样器。研究表明：对角元素和单位下三角元素的全条件分布分别服从单变量广义逆高斯分布和多元正态分布。虽然该问题亦可考虑采用梅特罗波利斯-哈斯廷斯算法的多种变体，但我们通过数学证明其平均接受率在特定场景下会变得极低。我们通过仿真研究和数据分析验证了所提吉布斯采样器的计算效率。