Mathematics – Probability
Scientific paper
May 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aipc..568...61a&link_type=abstract
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 20th International Workshop. AIP Conference Proceedi
Mathematics
Probability
Information Theory And Communication Theory, Probability Theory
Scientific paper
We discuss precise assumptions entailing Bayesianism in the line of investigations started by Cox, and relate them to a recent critique by Halpern. We show that every finite model which cannot be rescaled to probability violates a natural and simple refinability principle. A new condition, separability, was found sufficient and necessary for rescalability of infinite models. We finally characterize the acceptable ways to handle uncertainty in infinite models based on Cox's assumptions. Certain closure properties must be assumed before all the axioms of ordered fields are satisfied. Once this is done, a proper plausibility model can be embedded in an ordered fields containing the reals, namely either standard probability (field of reals) for a real valued plausibility model, or extended probability (field of reals and infinitesimals) for an ordered plausibility model. The end result is that if our assumptions are accepted, all reasonable uncertainty management schemes must be based on sets of extended probability distributions and Bayes conditioning. .
Arnborg S.
Sjödin G.
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