Inductive Inference: An Axiomatic Approach
AbstractA 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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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1339.
Length: 45 pages
Date of creation: Dec 2001
Date of revision:
Publication status: Published in Econometrica (2003) 71: 1-26
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," NajEcon Working Paper Reviews 391749000000000544, www.najecon.org.
- Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
- Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
- Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
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