On Nov 17, 2005, at 2:08 PM, Jason Palmer wrote: > It is my understanding that Bayesians also believe in fixed > distributions for given phenomena.
At least one major proponent of Bayesian methods -- E. T. Jaynes -- would strongly disagree with this statement, calling it an example of the "mind projection fallacy" [1]. Jaynes views probability theory as an extension of classical logical that can handle degrees of certainty between the two extremes "certainly true" and "certainly false," a view that is supported by Cox's Theorem [2,3]. Thus a Bayesian probability distribution represents only one's state of knowledge about some aspect of the physical world -- it is not a property of the physical world itself. The notion of "imprecise" probabilities is then nonsensical, as presupposes that there is some "correct", but unknown, distribution that is a property of some physical system. 1. E. T. Jaynes, Probability Theory: The Logic of Science. Cambridge University Press, 2003. 2. R. T. Cox, "Probability, frequency, and reasonable expectation." American Journal of Physics 17 (1946), 1--7. 3. K. S. Van Horn, "Constructing a logic of plausible inference: a guide to Cox's Theorem." International Journal of Approximate Reasoning 34, no. 1 (Sept. 2003); available on the web at http:// www.leuther-analytics.com/bayes/papers.html. _______________________________________________ uai mailing list [email protected] https://secure.engr.oregonstate.edu/mailman/listinfo/uai
