Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures
Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures
复制标题
DOI：
10.1214/22-ba1348
复制
发表时间：
2022-01
影响因子：
4.4
通讯作者：
Y. Hamura;Takahiro Onizuka;Shintaro Hashimoto;S. Sugasawa
中科院分区：
文献类型：
--
作者：
Y. Hamura;Takahiro Onizuka;Shintaro Hashimoto;S. Sugasawa
在各种应用中，我们处理通常表现出稀疏性的高维正值数据。本文开发了一类新的连续全局局部收缩先验，专门用于分析伽马分布观测值，其中大多数底层均值都集中在某个值附近。与现有的收缩先验不同，我们的新先验是逆伽马分布的形状尺度混合，它对后验均值的形式有理想的解释，并允许灵活的收缩。我们证明所提出的先验具有两个理想的理论特性； Kullback-Leibler 在稀疏性下的超效率和针对大型观测的稳健收缩规则。我们提出了一种用于后验推理的有效采样算法。通过模拟和两个真实数据示例（韩国 COVID-19 的平均住院时间和基因表达数据的自适应方差估计）说明了该方法的性能。
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.