论文标题
稀疏的贝叶斯对伽马分布观测的推断使用形状尺度的逆伽马混合物
Sparse Bayesian inference on gamma-distributed observations using shape-scale inverse-gamma mixtures
论文作者
论文摘要
在各种应用中，我们处理经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球收缩率先验，该研究量其量身定制，用于分析伽马分布的观测值，其中大多数基础均值集中在一定值周围。与现有的收缩先验不同，我们的新先验是反伽马分布的形状尺度混合物，该分布对后均值的形式有理想的解释，并承认柔性收缩。我们表明，提议的先验具有两个理想的理论特性。 kullback-leibler在稀疏性和强大的收缩规则下为大观测而言。我们提出了一种有效的采样算法，用于后推断。通过模拟和两个真实的数据示例来说明所提出的方法的性能，即韩国Covid-19的平均住院时间以及基因表达数据的自适应差异估计。
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.
