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ファイル | 記述 | サイズ | フォーマット | |
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10618600.2022.2119988.pdf | 1.65 MB | Adobe PDF | 見る/開く |
タイトル: | On Data Augmentation for Models Involving Reciprocal Gamma Functions |
著者: | Hamura, Yasuyuki Irie, Kaoru Sugasawa, Shonosuke |
著者名の別形: | 羽村, 靖之 |
キーワード: | Gauss’s multiplication formula Markov chain Monte Carlo reciprocal gamma function Stirling’s formula |
発行日: | Jul-2023 |
出版者: | Taylor & Francis Group |
誌名: | Journal of Computational and Graphical Statistics |
巻: | 32 |
号: | 3 |
開始ページ: | 908 |
終了ページ: | 916 |
抄録: | 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. |
著作権等: | © 2022 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. |
URI: | http://hdl.handle.net/2433/285116 |
DOI(出版社版): | 10.1080/10618600.2022.2119988 |
出現コレクション: | 学術雑誌掲載論文等 |
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