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Bayesian model diagnostics using functional Bregman divergence

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  • Goh, Gyuhyeong
  • Dey, Dipak K.

Abstract

It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are reasonable, given the substantive context of the model; and then examining the sensitivity of inferences to reasonable changes in the prior distribution and the likelihood. Here we consider functional Bregman divergence between posterior distributions for model diagnostics, which produce methods for outlier detection as well as for prior sensitivity analysis. The methodology is exemplified through a logistic regression and a circular data model.

Suggested Citation

  • Goh, Gyuhyeong & Dey, Dipak K., 2014. "Bayesian model diagnostics using functional Bregman divergence," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 371-383.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:371-383
    DOI: 10.1016/j.jmva.2013.11.008
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    References listed on IDEAS

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    1. Gelfand A. E. & Dey D. K., 1991. "On Bayesian Robustness Of Contaminated Classes Of Priors," Statistics & Risk Modeling, De Gruyter, vol. 9(1-2), pages 63-80, February.
    2. Dey, Dipak K. & Birmiwal, Lea R., 1994. "Robust Bayesian analysis using divergence measures," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 287-294, July.
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    Cited by:

    1. Spiridon Penev & Pavel Shevchenko & Wei Wu, 2019. "Myopic robust index tracking with Bregman divergence," Papers 1908.07659, arXiv.org, revised Jul 2021.
    2. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    3. Xiaoyue Zhao & Lin Zhang & Dipankar Bandyopadhyay, 2021. "A Shared Spatial Model for Multivariate Extreme-Valued Binary Data with Non-Random Missingness," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 374-396, November.
    4. Wang, Huan & Wang, Guan-jun & Duan, Feng-jun, 2016. "Planning of step-stress accelerated degradation test based on the inverse Gaussian process," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 97-105.

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