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Entropy 2013, 15(9), 3528-3591; doi:10.3390/e15093528

Objective Bayesianism and the Maximum Entropy Principle

Department of Philosophy, School of European Culture and Languages, University of Kent, Canterbury CT2 7NF, UK
* Author to whom correspondence should be addressed.
Received: 28 June 2013 / Revised: 21 August 2013 / Accepted: 21 August 2013 / Published: 4 September 2013
(This article belongs to the Special Issue Maximum Entropy and Bayes Theorem)
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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.
Keywords: objective Bayesianism; g-entropy; generalised entropy; Bayesian conditionalisation; scoring rule; maximum entropy; maxent; minimax objective Bayesianism; g-entropy; generalised entropy; Bayesian conditionalisation; scoring rule; maximum entropy; maxent; minimax
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Landes, J.; Williamson, J. Objective Bayesianism and the Maximum Entropy Principle. Entropy 2013, 15, 3528-3591.

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