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Processing consistency in non-Bayesian inference

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  • He, Xue Dong
  • Xiao, Di

Abstract

We propose a coherent inference model that is obtained by distorting the prior density in Bayes’ rule and replacing the likelihood with a so-called pseudo-likelihood. This model includes the existing non-Bayesian inference models as special cases and implies new models of base-rate neglect and conservatism. We prove a sufficient and necessary condition under which the coherent inference model is processing consistent, i.e., implies the same posterior density however the samples are grouped and processed retrospectively. We further show that processing consistency does not imply Bayes’ rule by proving a sufficient and necessary condition under which the coherent inference model can be obtained by applying Bayes’ rule to a false stochastic model.

Suggested Citation

  • He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    • Handle: RePEc:eee:mateco:v:70:y:2017:i:c:p:90-104
    DOI: 10.1016/j.jmateco.2017.02.004
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    1. Daniel J. Benjamin & Matthew Rabin & Collin Raymond, 2016. "A Model of Nonbelief in the Law of Large Numbers," Journal of the European Economic Association, European Economic Association, vol. 14(2), pages 515-544.
    2. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    3. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 775-816.
    4. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    5. Nicola Gennaioli & Andrei Shleifer, 2010. "What Comes to Mind," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(4), pages 1399-1433.
    6. , G. & , & ,, 2008. "Non-Bayesian updating: A theoretical framework," Theoretical Economics, Econometric Society, vol. 3(2), June.
    7. Ali Jadbabaie & Alvaro Sandroni & Alireza Tahbaz-Salehi, 2010. "Non-Bayesian Social Learning, Second Version," PIER Working Paper Archive 10-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Feb 2010.
    8. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 730-778.
    9. Epstein Larry G & Noor Jawwad & Sandroni Alvaro, 2010. "Non-Bayesian Learning," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-20, January.
    10. Larry G. Epstein, 2006. "An Axiomatic Model of Non-Bayesian Updating," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(2), pages 413-436.
    11. Pietro Ortoleva, 2012. "Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News," American Economic Review, American Economic Association, vol. 102(6), pages 2410-2436, October.
    12. Larry G. Epstein & Jawwad Noor & Alvaro Sandroni, 2008. "Supplementary Appendix for ‘Non-Bayesian Updating: A Theoretical Framework’," PIER Working Paper Archive 08-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Camerer, Colin F, 1987. "Do Biases in Probability Judgment Matter in Markets? Experimental Evidence," American Economic Review, American Economic Association, vol. 77(5), pages 981-997, December.
    14. Nelson, Mark W. & Bloomfield, Robert & Hales, Jeffrey W. & Libby, Robert, 2001. "The Effect of Information Strength and Weight on Behavior in Financial Markets," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 168-196, November.
    15. Matthew Rabin & Joel L. Schrag, 1999. "First Impressions Matter: A Model of Confirmatory Bias," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 37-82.
    16. Carlo Kraemer & Martin Weber, 2004. "How Do People Take into Account Weight, Strength and Quality of Segregated vs. Aggregated Data? Experimental Evidence," Journal of Risk and Uncertainty, Springer, vol. 29(2), pages 113-142, September.
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