  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.
