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Measuring Bayesian Robustness Using Rényi Divergence

Author

Listed:
  • Luai Al-Labadi

    (Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6, Canada)

  • Forough Fazeli Asl

    (Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran)

  • Ce Wang

    (Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6, Canada)

Abstract

This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighborhood of the elicited prior are considered. The first one is the well-known ϵ -contaminated class, while the second one is the geometric mixing class. The proposed measure of robustness is based on computing the curvature of Rényi divergence between posterior distributions. Examples are used to illustrate the results by using simulated and real data sets.

Suggested Citation

  • Luai Al-Labadi & Forough Fazeli Asl & Ce Wang, 2021. "Measuring Bayesian Robustness Using Rényi Divergence," Stats, MDPI, vol. 4(2), pages 1-18, March.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:2:p:18-268:d:525970
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    References listed on IDEAS

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    1. Bentes, Sónia R. & Menezes, Rui & Mendes, Diana A., 2008. "Long memory and volatility clustering: Is the empirical evidence consistent across stock markets?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3826-3830.
    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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