Bayesian influence analysis: a geometric approach.

TitleBayesian influence analysis: a geometric approach.
Publication TypeJournal Article
Year of Publication2011
AuthorsZhu, Hongtu, Joseph G. Ibrahim, and Niansheng Tang
JournalBiometrika
Volume98
Issue2
Pagination307-323
Date Published2011 Jun
ISSN0006-3444
Abstract

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.

DOI10.1093/biomet/asr009
Alternate JournalBiometrika
Original PublicationBayesian influence analysis: A geometric approach.
PubMed ID24453379
PubMed Central IDPMC3897258
Grant ListR01 CA074015-04A1 / CA / NCI NIH HHS / United States
R01 CA074015-09 / CA / NCI NIH HHS / United States
R21 AG033387-01A1 / AG / NIA NIH HHS / United States
R01 GM070335-07A1 / GM / NIGMS NIH HHS / United States
R01 CA074015-12 / CA / NCI NIH HHS / United States
P01 CA142538 / CA / NCI NIH HHS / United States
R01 CA074015-11A1 / CA / NCI NIH HHS / United States
R21 AG033387-02 / AG / NIA NIH HHS / United States
P01 CA142538-01 / CA / NCI NIH HHS / United States
R01 GM070335-12 / GM / NIGMS NIH HHS / United States
R01 CA074015-06 / CA / NCI NIH HHS / United States
R01 CA074015-05 / CA / NCI NIH HHS / United States
R01 MH086633-02 / MH / NIMH NIH HHS / United States
P01 CA142538-02 / CA / NCI NIH HHS / United States
R01 CA074015-03 / CA / NCI NIH HHS / United States
R01 GM070335-08 / GM / NIGMS NIH HHS / United States
R01 MH086633-03 / MH / NIMH NIH HHS / United States
R01 GM070335-10 / GM / NIGMS NIH HHS / United States
R01 CA070101-06 / CA / NCI NIH HHS / United States
R01 MH086633 / MH / NIMH NIH HHS / United States
R01 GM070335-09 / GM / NIGMS NIH HHS / United States
R01 CA074015-10 / CA / NCI NIH HHS / United States
R01 MH086633-01A1 / MH / NIMH NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States
R01 GM070335-11 / GM / NIGMS NIH HHS / United States
R01 CA070101-05 / CA / NCI NIH HHS / United States
R01 CA070101-04 / CA / NCI NIH HHS / United States
R01 CA074015-08A2 / CA / NCI NIH HHS / United States
R21 AG033387 / AG / NIA NIH HHS / United States
R01 CA074015-07 / CA / NCI NIH HHS / United States
R01 CA074015 / CA / NCI NIH HHS / United States
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