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Foundations of Info-MetricsModeling, Inference, and Imperfect Information$
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Amos Golan

Print publication date: 2017

Print ISBN-13: 9780199349524

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780199349524.001.0001

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Rational Inference

Rational Inference

A Constrained Optimization Framework

Chapter:
(p.10) 2 Rational Inference
Source:
Foundations of Info-Metrics
Author(s):

Amos Golan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199349524.003.0002

In this chapter I present arguments for the use of info-metrics as a fundamental framework for rational inference. The chapter consists of two interdependent parts. In the first I provide the framework for rational inference, which involves the use of a specific decision function to achieve the desired inference. In the second part I summarize four sets of axioms to justify the decision function argued for in the first part. All axioms lead to the same decision function: the entropy function of Boltzmann, Gibbs, and Shannon. In this chapter I emphasize underdetermined problems and problems of insufficient information, but I also discuss inference based on information resulting from repeated independent experiments. The same entropy function is identified in each case, as well as the desired decision function.

Keywords:   axioms for inference, constrained optimization, decision function, entropy, rational inference

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