On Data Augmentation for Models Involving Reciprocal Gamma Functions

Yasuyuki Hamura, Kaoru Irie, Shonosuke Sugasawa

Research output: Contribution to journalArticlepeer-review


In this article, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to approximate full conditional densities of shape parameters by using Gauss’s multiplication formula and Stirling’s formula for the gamma function, where the approximation error can be made arbitrarily small. We use the techniques to construct efficient Gibbs and Metropolis–Hastings algorithms for a variety of models that involve the gamma distribution, Student’s t-distribution, the Dirichlet distribution, the negative binomial distribution, and the Wishart distribution. The proposed sampling method is numerically demonstrated through simulation studies. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)908-916
Number of pages9
JournalJournal of Computational and Graphical Statistics
Issue number3
Publication statusPublished - 2023
Externally publishedYes


  • Gauss’s multiplication formula
  • Markov chain Monte Carlo
  • Reciprocal gamma function
  • Stirling’s formula

ASJC Scopus subject areas

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


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