An Axiomatic Framework for Belief Updates

David Heckerman

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arXiv · 1304.3091

An Axiomatic Framework for Belief Updates

David Heckerman

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Abstract

In the 1940's, a physicist named Cox provided the first formal justification for the axioms of probability based on the subjective or Bayesian interpretation. He showed that if a measure of belief satisfies several fundamental properties, then the measure must be some monotonic transformation of a probability. In this paper, measures of change in belief or belief updates are examined. In the spirit of Cox, properties for a measure of change in belief are enumerated. It is shown that if a measure satisfies these properties, it must satisfy other restrictive conditions. For example, it is shown that belief updates in a probabilistic context must be equal to some monotonic transformation of a likelihood ratio. It is hoped that this formal explication of the belief update paradigm will facilitate critical discussion and useful extensions of the approach.

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David Heckerman. 2013-03-27. An Axiomatic Framework for Belief Updates. https://arxiv.org/abs/1304.3091

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