Bayesian influence analysis: a geometric approach.
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.
Department of Biostatistics, CB# 7420, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27516, U.S.A., hzhu@bios.unc.edu , ibrahim@bios.unc.edu.
Hongtu
H
Zhu
Department of Biostatistics, CB# 7420, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27516, U.S.A., hzhu@bios.unc.edu , ibrahim@bios.unc.edu.
Joseph G
JG
Ibrahim
Department of Statistics, Yunnan University, Kunming 650091, P. R. China, nstang@bio.unc.edu.
Niansheng
N
Tang
Influence measure; Perturbation manifold; Perturbation model; Prior distribution