Gibbs Sampler for Matrix Generalized Inverse Gaussian Distributions

Yasuyuki Hamura, Kaoru Irie, Shonosuke Sugasawa

Research output: Contribution to journalArticlepeer-review

Abstract

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 Cholesky decomposition. We show that the full conditionals of the entries of the diagonal and unit lower-triangular matrices 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. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)331-340
Number of pages10
JournalJournal of Computational and Graphical Statistics
Volume33
Issue number2
DOIs
Publication statusPublished - 2024

Keywords

  • Markov chain Monte Carlo
  • Matrix generalized inverse Gaussian distributions
  • Matrix skew-t distributions
  • Partial Gaussian graphical models

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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