Zhu Hongtu, Ibrahim Joseph G, Tang Niansheng
Department of Biostatistics, CB# 7420, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27516, U.S.A.,
Department of Statistics, Yunnan University, Kunming 650091, P. R. China,
Biometrika. 2011 Jun;98(2):307-323. doi: 10.1093/biomet/asr009.
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.
在本文中，我们开发了一个贝叶斯影响分析的通用框架，用于评估针对一类统计模型的数据、先验和抽样分布的各种扰动方案。我们引入一个扰动模型来刻画这些不同的扰动方案。我们构建了一个称为贝叶斯扰动流形的几何框架，并使用其相关的几何量（包括度量张量和测地线）来刻画扰动模型的内在结构。我们基于贝叶斯扰动流形开发了内在影响度量和局部影响度量，以量化各种扰动对统计模型的影响。通过理论和数值示例来突出这种局部影响方法在形式化贝叶斯分析中的广泛应用。
