On the Definition of Objective Probabilities by Empirical Similarity

Itzhak Gilboa, Offer Lieberman, David Schmeidle

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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
Title of host publicationCase-Based Predictions
Subtitle of host publicationAn Axiomatic Approach to Prediction, Classification and Statistical Learning
PublisherTaylor and Francis
Pages259-280
Number of pages22
ISBN (Electronic)9789814366182
ISBN (Print)981436617X, 9789814366175
DOIs
StatePublished - 1 Jan 2012
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

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