Robust Bayesian Modeling of Counts with Zero Inflation and Outliers: Theoretical Robustness and Efficient Computation

• 成果类型: Article; Early Access
• 署名作者: Hamura, Yasuyuki; Irie, Kaoru; Sugasawa, Shonosuke
• 署名单位: Kyoto University; University of Tokyo; Keio University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2447111
• 发表日期: 2025
• 关键词: poisson regression; inference

摘要

Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such contamination. This study introduces a novel framework for Bayesian modeling of counts that is robust to both zero inflation and large outliers. In doing so, we introduce rescaled beta distribution and adopt it to absorb undesirable effects from zero and outlying counts. The proposed approach has two appealing features: the efficiency of the posterior computation via a custom Gibbs sampling algorithm and a theoretically guaranteed posterior robustness, where extreme outliers are automatically removed from the posterior distribution. We demonstrate the usefulness of the proposed method by applying it to trend filtering and spatial modeling using predictive Gaussian processes. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.