Title | Bayesian influence analysis: a geometric approach. |
Publication Type | Journal Article |
Year of Publication | 2011 |
Authors | Zhu, Hongtu, Joseph G. Ibrahim, and Niansheng Tang |
Journal | Biometrika |
Volume | 98 |
Issue | 2 |
Pagination | 307-323 |
Date Published | 2011 Jun |
ISSN | 0006-3444 |
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. |
DOI | 10.1093/biomet/asr009 |
Alternate Journal | Biometrika |
Original Publication | Bayesian influence analysis: A geometric approach. |
PubMed ID | 24453379 |
PubMed Central ID | PMC3897258 |
Grant List | R01 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 |
Bayesian influence analysis: a geometric approach.
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