TY - JOUR

T1 - On the definition of objective probabilities by empirical similarity

AU - Gilboa, Itzhak

AU - Lieberman, Offer

AU - Schmeidler, David

N1 - Funding Information:
Acknowledgements We wish to thank Gabi Gayer, Jacob Leshno, Arik Roginsky, Idan Shimony, and an anonymous referee for comments and references. This project was supported by the Pinhas Sapir Center for Development and Israel Science Foundation Grants Nos. 975/03 and 355/06.

PY - 2010/1

Y1 - 2010/1

N2 - We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

AB - We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

KW - Case-based reasoning

KW - Frequentist approach

KW - Objective probability

KW - Similarity

UR - http://www.scopus.com/inward/record.url?scp=77349111548&partnerID=8YFLogxK

U2 - 10.1007/s11229-009-9473-4

DO - 10.1007/s11229-009-9473-4

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AN - SCOPUS:77349111548

SN - 0039-7857

VL - 172

SP - 79

EP - 95

JO - Synthese

JF - Synthese

IS - 1

ER -