Bayesian influence analysis: a geometric approach

• 成果类型: Article
• 署名作者: Zhu, Hongtu; Ibrahim, Joseph G.; Tang, Niansheng
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Yunnan University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr009
• 发表日期: 2011
• 页码: 307323
• 关键词: local influence; divergence measures; sensitivity; models; diagnostics; perturbation

摘要

In this paper we develop a general framework of Bayesian influence analysis for assessing various perturbation schemes to the data, the prior and the sampling distribution for a class of statistical models. We introduce a perturbation model to characterize these various perturbation schemes. We develop a geometric framework, called the Bayesian perturbation manifold, and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model. We develop intrinsic influence measures and local influence measures based on the Bayesian perturbation manifold to quantify the effect of various perturbations to statistical models. Theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal Bayesian analysis.