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 language | English |
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Pages (from-to) | 79-95 |
Number of pages | 17 |
Journal | Synthese |
Volume | 172 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2010 |
Externally published | Yes |
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.
Funders | Funder number |
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Pinhas Sapir Center for Development and Israel Science Foundation | 355/06, 975/03 |
Keywords
- Case-based reasoning
- Frequentist approach
- Objective probability
- Similarity