Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling

• 成果类型: Article
• 署名作者: Chang, Jinyuan; Tang, Cheng Yong; Zhu, Yuanzheng
• 署名单位: Southwestern University of Finance & Economics - China; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; Southwestern University of Finance & Economics - China
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf009
• 发表日期: 2025
• 页码: 1127-1149
• 关键词: scope

摘要

In this study, we introduce a novel methodological framework called Bayesian penalized empirical likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.