• For sparse positive-valued data, a novel Bayesian hierarchical model was proposed. 
• It was shown that the proposed method has desirable theoretical properties.
• An efficient Markov chain Monte Carlo algorithm to compute posterior distribution was proposed. 
• The proposed method was applied to data analysis of average length of hospital stay for COVID-19 in South Korea.  

In various statistical applications, we often face a sequence of positive-valued observations such as machine failure time, store waiting time, survival time under a certain disease, an income of a certain group, and so on. A common feature of the data is “sparsity” in the sense that most of the underlying means of observations are concentrated around a certain value (grand mean) while a small part of the means is significantly away from the grand mean. 

In this paper, we proposed a Bayesian hierarchical model based on gamma-distributed observations. It was shown that the proposed method has two desirable theoretical properties; (i) Kullback-Leibler super-efficiency under sparsity and (ii) robust shrinkage rules for large observations. An efficient sampling algorithm for posterior inference was also provided. 

The performance of the proposed method was 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.

Paper Info
Yasuyuki Hamura, Takahiro Onizuka, Shintaro Hashimoto and Shonosuke Sugasawa, "Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures", Bayesian Anal. Advance Publication 1-21, 2022.

 https://doi.org/10.1214/22-BA1348