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.

翻译：在各种应用中,我们处理的往往是显示宽度的高维正值数据。本文发展了一套新的连续的全球-局部缩水前科,专门用来分析大部分基本手段集中在某一价值范围内的伽马分布观测。与现有的缩水前科不同,我们的新前科是反伽马分布的形状比例混合,对后方平均值的形式有可取的解释,并承认灵活的缩水。我们表明,先前的提议有两个可取的理论属性:宽度下的Kullback-Lebell超级效率,以及大型观测的稳健缩缩水规则。我们提出了后方推断的有效抽样算法。拟议方法的绩效通过模拟和两个真实数据实例,即韩国COVID-19住院的平均时间和对基因表达数据的适应性差异估计来加以说明。