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Inductive Inference: An Axiomatic Approach

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  • Itzhak Gilboa

    (Tel Aviv University)

  • David Schmeidler

    (Tel Aviv University)

Abstract

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality-case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality-case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions.

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File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1339.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1339.

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Length: 45 pages
Date of creation: Dec 2001
Date of revision:
Publication status: Published in Econometrica (2003) 71: 1-26
Handle: RePEc:cwl:cwldpp:1339

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Related research

Keywords: Inductive inference; case-based reasoning; case-based decision theory; maximum likelihood;

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