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

التفاصيل البيبلوغرافية
العنوان: Sparse Bayesian inference on gamma-distributed observations using shape-scale inverse-gamma mixtures
المؤلفون: Hamura, Yasuyuki, Onizuka, Takahiro, Hashimoto, Shintaro, Sugasawa, Shonosuke
سنة النشر: 2022
المجموعة: Statistics
مصطلحات موضوعية: Statistics - Methodology
الوصف: 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.
Comment: 57 pages, 8 figures
نوع الوثيقة: Working Paper
DOI: 10.1214/22-ba1348
URL الوصول: http://arxiv.org/abs/2203.08440
رقم الأكسشن: edsarx.2203.08440
قاعدة البيانات: arXiv