IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v164y2020ics016771522030105x.html
   My bibliography  Save this article

Departing from Bayesian inference toward minimaxity to the extent that the posterior distribution is unreliable

Author

Listed:
  • Bickel, David R.

Abstract

A Bayesian model may be relied on to the extent of its adequacy by minimizing the posterior expected loss raised to the power of a discounting exponent. The resulting action is minimax under broad conditions when the sample size is held fixed and the discounting exponent is infinite. On the other hand, for any finite discounting exponent, the action is Bayes when the sample size is sufficiently large. Thus, the action is Bayes when there is enough reliable information in the posterior distribution, is minimax when the posterior distribution is completely unreliable, and is a continuous blend of the two extremes otherwise.

Suggested Citation

  • Bickel, David R., 2020. "Departing from Bayesian inference toward minimaxity to the extent that the posterior distribution is unreliable," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s016771522030105x
    DOI: 10.1016/j.spl.2020.108802
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522030105X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108802?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel J. Benjamin & James O. Berger & Magnus Johannesson & Brian A. Nosek & E.-J. Wagenmakers & Richard Berk & Kenneth A. Bollen & Björn Brembs & Lawrence Brown & Colin Camerer & David Cesarini & Chr, 2018. "Redefine statistical significance," Nature Human Behaviour, Nature, vol. 2(1), pages 6-10, January.
      • Daniel Benjamin & James Berger & Magnus Johannesson & Brian Nosek & E. Wagenmakers & Richard Berk & Kenneth Bollen & Bjorn Brembs & Lawrence Brown & Colin Camerer & David Cesarini & Christopher Chambe, 2017. "Redefine Statistical Significance," Artefactual Field Experiments 00612, The Field Experiments Website.
    2. David Bickel, 2015. "Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 523-546, November.
    3. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, 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. Simone Cerreia-Vioglio & Fulvio Ortu & Federico Severino & Claudio Tebaldi, 2017. "Multivariate Wold Decompositions," Working Papers 606, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    3. John Y. Campbell, 2016. "Restoring Rational Choice: The Challenge of Consumer Financial Regulation," American Economic Review, American Economic Association, vol. 106(5), pages 1-30, May.
    4. Robert J. Shiller, 2005. "The Life-Cycle Personal Accounts Proposal for Social Security: An Evaluation," Cowles Foundation Discussion Papers 1504, Cowles Foundation for Research in Economics, Yale University.
    5. Dreber, Anna & Heikensten, Emma & Säve-Söderbergh, Jenny, 2022. "Why do women ask for less?," Labour Economics, Elsevier, vol. 78(C).
    6. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    7. Eduardo Perez & Delphine Prady, 2012. "Complicating to Persuade?," Working Papers hal-03583827, HAL.
    8. Romain Blanchard & Laurence Carassus & Miklós Rásonyi, 2018. "No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 241-281, October.
    9. René Aïd & Matteo Basei & Giorgia Callegaro & Luciano Campi & Tiziano Vargiolu, 2020. "Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 205-232, February.
    10. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.
    11. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    12. John Y. Campbell & Luis M. Viceira & Joshua S. White, 2003. "Foreign Currency for Long-Term Investors," Economic Journal, Royal Economic Society, vol. 113(486), pages 1-25, March.
    13. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working Papers id:10795, eSocialSciences.
    14. Luçon, Eric, 2020. "Quenched asymptotics for interacting diffusions on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6783-6842.
    15. Lashi Bandara & Paul Bryan, 2020. "Heat kernels and regularity for rough metrics on smooth manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 293(12), pages 2255-2270, December.
    16. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    17. John A. List, 2024. "Optimally generate policy-based evidence before scaling," Nature, Nature, vol. 626(7999), pages 491-499, February.
    18. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    19. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    20. Amarante, Massimiliano & Ghossoub, Mario & Phelps, Edmund, 2015. "Ambiguity on the insurer’s side: The demand for insurance," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 61-78.

    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:eee:stapro:v:164:y:2020:i:c:s016771522030105x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.