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Robust Bayesian analysis using divergence measures

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  • Dey, Dipak K.
  • Birmiwal, Lea R.

Abstract

We consider the problem of measuring Bayesian robustness of classes of contaminated priors. Two classes of priors in the neighborhood of the elicited prior are considered, one is the usual [var epsilon]-contaminated class and the other one is a geometric mixing class. A global measure, using [phi]-divergence of the posterior distributions and its curvature, is introduced. Calculation of ranges of the curvatures are demonstrated through examples. It is shown that the curvature formulas give unified answers irrespective of the choice of the [phi]-functions. It is also observed that the variation of the posterior divergence measures and their curvature are especially useful for multidimensional problems.

Suggested Citation

  • Dey, Dipak K. & Birmiwal, Lea R., 1994. "Robust Bayesian analysis using divergence measures," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 287-294, July.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:4:p:287-294
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    Citations

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    Cited by:

    1. Adriano Suzuki & Vicente Cancho & Francisco Louzada, 2016. "The Poisson–Inverse-Gaussian regression model with cure rate: a Bayesian approach and its case influence diagnostics," Statistical Papers, Springer, vol. 57(1), pages 133-159, March.
    2. Haiyan Zheng & Thomas Jaki & James M.S. Wason, 2023. "Bayesian sample size determination using commensurate priors to leverage preexperimental data," Biometrics, The International Biometric Society, vol. 79(2), pages 669-683, June.
    3. Goh, Gyuhyeong & Dey, Dipak K., 2014. "Bayesian model diagnostics using functional Bregman divergence," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 371-383.
    4. Luai Al-Labadi & Forough Fazeli Asl & Ce Wang, 2021. "Measuring Bayesian Robustness Using Rényi Divergence," Stats, MDPI, vol. 4(2), pages 1-18, March.
    5. Giles Hooker & Anand Vidyashankar, 2014. "Bayesian model robustness via disparities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 556-584, September.
    6. Abhik Ghosh & Ayanendranath Basu, 2016. "Robust Bayes estimation using the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 413-437, April.
    7. Basu, Sanjib, 2000. "Uniform stability of posteriors," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 53-58, January.
    8. Gyuhyeong Goh & Jae Kwang Kim, 2021. "Accounting for model uncertainty in multiple imputation under complex sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 930-949, September.

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