NDLI: Objective Bayesianism and the Maximum Entropy Principle

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Objective Bayesianism and the Maximum Entropy Principle

Content Provider	MDPI
Author	Landes, Jürgen Williamson, Jon
Abstract	Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.
File Size	749568
Ending Page	3591
Page Count	64
Starting Page	3528
File Format	PDF
e-ISSN	10994300
DOI	10.3390/e15093528
Journal	Entropy
Issue Number	9
Volume Number	15
Language	English
Publisher Date	2013-09-04
Access Restriction	Open
Subject Keyword	objective Bayesianism g-entropy generalised entropy Bayesian conditionalisation scoring rule maximum entropy maxent minimax
Content Type	Text
Resource Type	Article

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