IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v4y2021i2p18-268d525970.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/4/2/18/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/4/2/18/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Salois, Matthew & Moss, Charles, 2010. "An Information Approach to the Dynamics in Farm Income: Implications for Farmland Markets," MPRA Paper 26850, University Library of Munich, Germany.
    2. Hull, Matthew & McGroarty, Frank, 2014. "Do emerging markets become more efficient as they develop? Long memory persistence in equity indices," Emerging Markets Review, Elsevier, vol. 18(C), pages 45-61.
    3. Pirino, Davide, 2009. "Jump detection and long range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1150-1156.
    4. Delgado-Bonal, Alfonso & López, Álvaro García, 2021. "Quantifying the randomness of the forex market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    5. Dejan Živkov & Jovan Njegić & Vera Mirović, 2016. "Dynamic Nexus between Exchange Rate and Stock Prices in the Major East European Economies," Prague Economic Papers, Prague University of Economics and Business, vol. 2016(6), pages 686-705.
    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. Bentes, Sónia R., 2014. "Measuring persistence in stock market volatility using the FIGARCH approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 190-197.
    8. Basu, Sanjib, 2000. "Uniform stability of posteriors," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 53-58, January.
    9. Galip Gençyürk, 2024. "Volatility Modeling and Spillover: The Turkish and Russian Stock Markets," Istanbul Business Research, Istanbul University Business School, vol. 53(1), pages 81-101, April.
    10. Yin, Yi & Shang, Pengjian & Ahn, Andrew C. & Peng, Chung-Kang, 2019. "Multiscale joint permutation entropy for complex time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 388-402.
    11. Shahzad, Syed Jawad Hussain & Nor, Safwan Mohd & Mensi, Walid & Kumar, Ronald Ravinesh, 2017. "Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 351-363.
    12. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
    13. Yin, Yi & Shang, Pengjian, 2016. "Weighted permutation entropy based on different symbolic approaches for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 137-148.
    14. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    15. Sun, Lin, 2013. "Pricing currency options in the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3441-3458.
    16. Zunino, Luciano & Fernández Bariviera, Aurelio & Guercio, M. Belén & Martinez, Lisana B. & Rosso, Osvaldo A., 2012. "On the efficiency of sovereign bond markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4342-4349.
    17. Omid Jenabi & Nazar Dahmardeh Ghale No, 2018. "Option Pricing in Stochastic Volatility Models Driven by Fractional Jump-Diffusion Processes," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 8(1), pages 1374-1374.
    18. Ahmadian, D. & Ballestra, L.V. & Shokrollahi, F., 2022. "A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    19. Carlos David Cardona-Arenas & Rafael Gómez-Gómez & Eliana Morales-Zuluaga, 2023. "COVID-19 and its short-term informational impact on the stock markets of the Pacific Alliance countries," SN Business & Economics, Springer, vol. 3(5), pages 1-23, May.
    20. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:4:y:2021:i:2:p:18-268:d:525970. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.