An axiomatic framework for belief updates
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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.
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| 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 + |
| Institution | Knowledge Systems, AI Laboratory + |
| Key | KSL-86-16 + |
| Month | February + |
| Note | 6 pages. + |
| Number | KSL-86-16 + |
| Tag | Computer science + |
| Title | An Axiomatic Framework for Belief Updates + |
| Tr id | KSL-86-16 + |
| Year | 1986 + |
