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Analogies and TheoriesFormal Models of Reasoning$
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Itzhak Gilboa, Larry Samuelson, and David Schmeidler

Print publication date: 2015

Print ISBN-13: 9780198738022

Published to Oxford Scholarship Online: May 2015

DOI: 10.1093/acprof:oso/9780198738022.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 07 March 2021

Inductive Inference

Inductive Inference

An Axiomatic Approach

(p.17) 2 Inductive Inference
Analogies and Theories

Itzhak Gilboa

Larry Samuelson

David Schmeidler

Oxford University Press

This chapter focuses on case-based reasoning. It offers an axiomatic approach to the following problem: given a database of observations, how should different eventualities be ranked? The approach is complementary to the Bayesian approach at two levels: first, it may offer an alternative model of prediction, when the information available to the predictor is not easily translated to the language of a prior probability. Second, the approach may describe how a prior is generated. The chapter is organized as follows. Section 2 presents the formal model and the main results. Section 3 discusses the relationship to kernel methods and to maximum likelihood rankings. Section 4 presents a critical discussion of the axioms, outlining their scope of application. Finally, Section 5 briefly discusses alternative interpretations of the model, and, in particular, relates it to case‐based decision theory.

Keywords:   case‐based reasoning, observations, Bayesian approach, prediction, kernel methods, maximum likelihood ranking, axioms, decision theory

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