2013/03/27 by David Heckerman, Heckerman, David
Computer Science · Decision Sciences · Mathematics · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Fuzzy Systems and Optimization #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.1304.3091
openalex publication_date 2013/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.