An Axiomatic Framework for Belief Updates
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.
Keywords: Axioms of Probability, Bayesian, Belief Updates
PDF Link: /papers/86/p123-heckerman.pdf
AUTHOR = "David Heckerman
TITLE = "An Axiomatic Framework for Belief Updates",
BOOKTITLE = "Proceedings of the Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-86)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1986",
PAGES = "123--128"