On Data Augmentation for Models Involving Reciprocal Gamma Functions

Autor:	Hamura, Yasuyuki, Irie, Kaoru, Sugasawa, Shonosuke
Rok vydání:	2022
Předmět:	Statistics - Methodology Statistics - Computation
Druh dokumentu:	Working Paper
DOI:	10.1080/10618600.2022.2119988
Popis:	In this paper, 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. Comment: 41 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.01704 Zobrazit plný text záznamu View this record from Arxiv