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タイトル: | Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures |
著者: | Hamura, Yasuyuki Onizuka, Takahiro Hashimoto, Shintaro Sugasawa, Shonosuke |
著者名の別形: | 羽村, 靖之 |
キーワード: | gamma distribution Kullback-Leibler super-efficiency Markov chain Monte Carlo tail-robustness |
発行日: | Mar-2024 |
出版者: | Institute of Mathematical Statistics |
誌名: | Bayesian Analysis |
巻: | 19 |
号: | 1 |
開始ページ: | 77 |
終了ページ: | 97 |
抄録: | In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where most of the underlying means are concentrated around a certain value. Unlike existing shrinkage priors, our new prior is a shape-scale mixture of inverse-gamma distributions, which has a desirable interpretation of the form of posterior mean and admits flexible shrinkage. We show that the proposed prior has two desirable theoretical properties; Kullback-Leibler super-efficiency under sparsity and robust shrinkage rules for large observations. We propose an efficient sampling algorithm for posterior inference. The performance of the proposed method is illustrated through simulation and two real data examples, the average length of hospital stay for COVID-19 in South Korea and adaptive variance estimation of gene expression data. |
著作権等: | © 2024 International Society for Bayesian Analysis Creative Commons Attribution 4.0 International License. |
URI: | http://hdl.handle.net/2433/286775 |
DOI(出版社版): | 10.1214/22-ba1348 |
出現コレクション: | 学術雑誌掲載論文等 |
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