IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v8y2011i2p117-127.html

Using Bayes' Rule to Update an Event's Probabilities Based on the Outcomes of Partially Similar Events

Author

Listed:
  • Robert F. Bordley

    (General Motors Technical Center, Warren, Michigan 48090; and University of Michigan, Ann Arbor, Michigan 48019)

Abstract

There is a widely known Bayesian solution to the problem of updating the probability of an event occurring given information on the outcome of n completely similar events. But in many, if not most, cases, we only have information on partially similar events. For example, firms must assess the probability of a new product being successful given information on past products that are only partially similar to the new product. This paper shows how the well-known Bayesian solution for completely similar events can be extended to solve the problem with partially similar past events.

Suggested Citation

  • Robert F. Bordley, 2011. "Using Bayes' Rule to Update an Event's Probabilities Based on the Outcomes of Partially Similar Events," Decision Analysis, INFORMS, vol. 8(2), pages 117-127, June.
    • Handle: RePEc:inm:ordeca:v:8:y:2011:i:2:p:117-127
    DOI: 10.1287/deca.1110.0204
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.1110.0204
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.1110.0204?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
    ---><---

    References listed on IDEAS

    as
    1. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 2009. "Proper Scoring Rules, Dominated Forecasts, and Coherence," Decision Analysis, INFORMS, vol. 6(4), pages 202-221, December.
    2. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    3. Bordley, Robert F, 1993. "Estimating Automotive Elasticities from Segment Elasticities and First Choice/Second Choice Data," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 455-462, August.
    4. Aurélien Baillon, 2008. "Eliciting Subjective Probabilities Through Exchangeable Events: An Advantage and a Limitation," Decision Analysis, INFORMS, vol. 5(2), pages 76-87, June.
    5. Robert F. Bordley, 2009. "Combining the Opinions of Experts Who Partition Events Differently," Decision Analysis, INFORMS, vol. 6(1), pages 38-46, March.
    6. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2012. "Axiomatization of an Exponential Similarity Function," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 10, pages 245-257, World Scientific Publishing Co. Pte. Ltd..
    7. Jason R. W. Merrick, 2008. "Getting the Right Mix of Experts," Decision Analysis, INFORMS, vol. 5(1), pages 43-52, March.
    8. Ali E. Abbas & David V. Budescu & Hsiu-Ting Yu & Ryan Haggerty, 2008. "A Comparison of Two Probability Encoding Methods: Fixed Probability vs. Fixed Variable Values," Decision Analysis, INFORMS, vol. 5(4), pages 190-202, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. L. Robin Keller & Kelly M. Kophazi, 2011. "From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating," Decision Analysis, INFORMS, vol. 8(2), pages 83-87, June.
    2. Mohrschladt, Hannes & Langer, Thomas, 2020. "Biased information weight processing in stock markets," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 89-106.
    3. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback," Decision Analysis, INFORMS, vol. 10(1), pages 1-5, March.
    4. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
    5. L. Robin Keller, 2011. "From the Editor ---Multiattribute and Intertemporal Preferences, Probability, and Stochastic Processes: Models and Assessment," Decision Analysis, INFORMS, vol. 8(3), pages 165-169, September.
    6. L. Robin Keller & Kelly M. Kophazi, 2012. "From the Editors ---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics," Decision Analysis, INFORMS, vol. 9(3), pages 213-218, September.
    7. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.

    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. L. Robin Keller, 2011. "From the Editor ---Multiattribute and Intertemporal Preferences, Probability, and Stochastic Processes: Models and Assessment," Decision Analysis, INFORMS, vol. 8(3), pages 165-169, September.
    2. L. Robin Keller & Kelly M. Kophazi, 2012. "From the Editors ---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics," Decision Analysis, INFORMS, vol. 9(3), pages 213-218, September.
    3. L. Robin Keller & Kelly M. Kophazi, 2011. "From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating," Decision Analysis, INFORMS, vol. 8(2), pages 83-87, June.
    4. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
    5. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback," Decision Analysis, INFORMS, vol. 10(1), pages 1-5, March.
    6. L. Robin Keller & Kelly M. Kophazi, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(2), pages 151-154, June.
    7. Robert F. Bordley & Elena Katok & L. Robin Keller, 2010. "Honoring Michael H. Rothkopf's Legacy of Rigor and Relevance in Auction Theory: From the Editors," Decision Analysis, INFORMS, vol. 7(1), pages 1-4, March.
    8. L. Robin Keller, 2009. "From the Editor..," Decision Analysis, INFORMS, vol. 6(1), pages 1-3, March.
    9. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.
    10. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    11. L. Robin Keller & Ali Abbas & Manel Baucells & Vicki M. Bier & David Budescu & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Ahti Salo & George Wu, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(4), pages 327-330, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
      • L. Robin Keller & Manel Baucells & Kevin F. McCardle & Gregory S. Parnell & Ahti Salo, 2007. "From the Editors..," Decision Analysis, INFORMS, vol. 4(4), pages 173-175, December.
    12. Yuyu Fan & David V. Budescu & David Mandel & Mark Himmelstein, 2019. "Improving Accuracy by Coherence Weighting of Direct and Ratio Probability Judgments," Decision Analysis, INFORMS, vol. 16(3), pages 197-217, September.
    13. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors ---Group Decisions, Preference Elicitation, Experienced Utility, Survival Probabilities, and Portfolio Value of Information," Decision Analysis, INFORMS, vol. 10(2), pages 99-102, June.
    14. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.
    15. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
    16. Jason R. W. Merrick & Fabrizio Ruggeri & Refik Soyer & L. Robin Keller, 2012. "From the Editors---Games and Decisions in Reliability and Risk," Decision Analysis, INFORMS, vol. 9(2), pages 81-85, June.
    17. David Kaplan & Jianshen Chen, 2012. "A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 581-609, July.
    18. repec:awi:wpaper:0470 is not listed on IDEAS
    19. Todd Guilfoos & Andreas Duus Pape, 2020. "Estimating Case-Based Learning," Games, MDPI, vol. 11(3), pages 1-25, September.
    20. Julia R. Falconer & Eibe Frank & Devon L. L. Polaschek & Chaitanya Joshi, 2022. "Methods for Eliciting Informative Prior Distributions: A Critical Review," Decision Analysis, INFORMS, vol. 19(3), pages 189-204, September.
    21. Chiang, Mi-Hsiu & Chiu, Hsin-Yu & Kuo, Wei-Yu, 2021. "Predictive ability of similarity-based futures trading strategies," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:inm:ordeca:v:8:y:2011:i:2:p:117-127. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.