Sparse Bayesian inference on gamma-distributed observations using shape-scale inverse-gamma mixtures

TL;DR

This paper introduces a novel shape-scale mixture of inverse-gamma priors for gamma-distributed data, enabling flexible and theoretically sound Bayesian inference in high-dimensional sparse settings.

Contribution

It develops a new class of global-local shrinkage priors with desirable properties for gamma data, including super-efficiency and robust shrinkage, along with an efficient sampling algorithm.

Findings

Demonstrates superior performance in simulations

Achieves accurate inference on COVID-19 hospital stay data

Effective adaptive variance estimation in gene expression

Abstract

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.