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On the foundations of Bayesianism
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2000 (English)Conference paper (Refereed)
Abstract [en]

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 nite model which cannot be rescaled to probability violates a natural and simple re nability principle. A new condition, separability, was found sufficient and necessary for rescalability of in nite models. We nally characterize the acceptable ways to handle uncertainty in in nite models based on Cox's assumptions. Certain closure properties must be assumed before all the axioms of ordered elds are satis ed. Once this is done, a proper plausibility model can be embedded in an ordered eld containing the reals, namely either standard probability ( eld of reals) for a real valued plausibility model, or extended probability ( eld of reals and in nitesimals) 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.

Place, publisher, year, edition, pages
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Computer and Information Science
URN: urn:nbn:se:kth:diva-58730OAI: diva2:473858
NR 20140805Available from: 2012-01-08 Created: 2012-01-08Bibliographically approved

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Arnborg, Stefan
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Numerical Analysis and Computer Science, NADA
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