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A0968
Title: Gibbs sampler for matrix generalized inverse Gaussian distributions Authors:  Kaoru Irie - University of Tokyo (Japan) [presenting]
Shonosuke Sugasawa - Keio University (Japan)
Yasuyuki Hamura - Kyoto University (Japan)
Abstract: Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. Here a novel blocked Gibbs sampler is proposed for the MGIG distributions based on the Choleski decomposition. It is shown 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 the average acceptance rates are mathematically proved that become extremely low in particular scenarios. The computational efficiency of the proposed Gibbs sampler is demonstrated through simulation studies and data analysis.