On the definition of objective probabilities by empirical similarity

Itzhak Gilboa, Offer Lieberman, David Schmeidler

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)79-95
Number of pages17
JournalSynthese
Volume172
Issue number1
DOIs
StatePublished - Jan 2010
Externally publishedYes

Bibliographical note

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.

Funding

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.

FundersFunder number
Pinhas Sapir Center for Development and Israel Science Foundation355/06, 975/03

    Keywords

    • Case-based reasoning
    • Frequentist approach
    • Objective probability
    • Similarity

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