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Bayesian influence analysis: a geometric approach

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  • Hongtu Zhu
  • Joseph G. Ibrahim
  • Niansheng Tang

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. Copyright 2011, Oxford University Press.

Suggested Citation

  • Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang, 2011. "Bayesian influence analysis: a geometric approach," Biometrika, Biometrika Trust, vol. 98(2), pages 307-323.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:307-323
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    File URL: http://hdl.handle.net/10.1093/biomet/asr009
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    Citations

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    Cited by:

    1. Niansheng Tang & Sy-Miin Chow & Joseph G. Ibrahim & Hongtu Zhu, 2017. "Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 875-903, December.
    2. Tang, Niansheng & Wu, Ying & Chen, Dan, 2018. "Semiparametric Bayesian analysis of transformation linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 225-240.
    3. Zhang, Yan-Qing & Tang, Nian-Sheng, 2017. "Bayesian local influence analysis of general estimating equations with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 184-200.
    4. Tsionas, Mike G., 2018. "Bayesian local influence analysis: With an application to stochastic frontiers," Economics Letters, Elsevier, vol. 165(C), pages 54-57.
    5. Indranil Ghosh & Kathleen Fleming, 2022. "On the Robustness and Sensitivity of Several Nonparametric Estimators via the Influence Curve Measure: A Brief Study," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    6. Yuanyuan Ju & Yan Yang & Mingxing Hu & Lin Dai & Liucang Wu, 2022. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    7. Xiaowen Dai & Libin Jin & Maozai Tian & Lei Shi, 2019. "Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity," Statistical Papers, Springer, vol. 60(5), pages 1423-1446, October.
    8. Ouyang, Ming & Yan, Xiaodong & Chen, Ji & Tang, Niansheng & Song, Xinyuan, 2017. "Bayesian local influence of semiparametric structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 102-115.
    9. Ming Ouyang & Xinyuan Song, 2020. "Bayesian Local Influence of Generalized Failure Time Models with Latent Variables and Multivariate Censored Data," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 298-316, July.
    10. Tang, Nian-Sheng & Duan, Xing-De, 2014. "Bayesian influence analysis of generalized partial linear mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 86-99.
    11. Abhijoy Saha & Sebastian Kurtek, 2019. "Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 104-143, February.

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