An Axiomatic Framework for Belief Updates

Citation: David Heckerman. (1986) An Axiomatic Framework for Belief Updates. In KSL-86-16, February,1986.

Publication techreport ( Edit )
type	Technical Report
bibtype	techreport
Bibtex basics
author	David Heckerman
title	An Axiomatic Framework for Belief Updates
number	KSL-86-16
institution	Knowledge Systems, AI Laboratory
year	1986
month	February
Bibtex more
note	6 pages.
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abstract	In the 1940's, a physicist named Cox provided the first formal justification from 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.

KSL Technical Report ID: KSL-86-16

Abstract	In the 1940's, a physicist named Cox provi … In the 1940's, a physicist named Cox provided the first formal justification from 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. ion and useful extensions of the approach.
Author	David Heckerman +
Bibtype	techreport +
Has author	David Heckerman +
Has identifier	KSL-86-16 +
Has publishing details	February,1986 +
Has title	An Axiomatic Framework for Belief Updates +
Has where published	KSL-86-16 +
Has year	1986 +
Institution	Knowledge Systems, AI Laboratory +
Ksl tr id	KSL-86-16 +
Month	February +
Note	6 pages.
Number	KSL-86-16 +
Process note	YES +
Title	An Axiomatic Framework for Belief Updates +
Year	1986 +