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Dynamics of Inductive Inference in a Unified Framework

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  • Itzhak Gilboa

    ()
    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959, Tel-Aviv University - Tel-Aviv University, Cowles Foundation for Research in Economics - Université Yale - New Haven)

  • Larry Samuelson

    (Department of Economics - Yale University)

  • David Schmeidler

    (Department of Cell and Developmental Biology - Tel Aviv University - Sackler Faculty of Medicine, The Ohio State University - The Ohio State University)

Abstract

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This uni ed framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.

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Paper provided by HAL in its series Working Papers with number hal-00712823.

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Date of creation: 28 Jun 2012
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Handle: RePEc:hal:wpaper:hal-00712823

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Keywords: dynamics; inductive inference; uni ed framework;

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  1. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
  3. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, April.
  4. Alquist, Ron & Kilian, Lutz, 2007. "What Do We Learn from the Price of Crude Oil Futures?," CEPR Discussion Papers 6548, C.E.P.R. Discussion Papers.
  5. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
  6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117, April.
  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  8. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Hume, David, 1758. "An Equiry Concerning Human Understanding," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number hume1758.
  10. Itzhak Gilboa & Larry Samuelson, 2012. "Subjectivity in Inductive Inference," Post-Print hal-00489433, HAL.
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