 Inductive Inference: An Axiomatic ApproachItzhak Gilboa and David Schmeidler Post-Print from HAL 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. Keywords: case-based reasoning; case-based decision theory; prediction; maximum likelihood; kernel functions; kernel classification (search for similar items in EconPapers) Published in Econometrica, 2003, Vol.71, n°1, pp.1-26. ⟨10.1111/1468-0262.00388⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00481297 Access Statistics for this paper More papers in Post-Print from HAL |
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