Objective Bayesianism and the Maximum Entropy Principle
Objective Bayesianism and the Maximum Entropy Principle
复制标题
客观贝叶斯主义和最大熵原理
作者：
J. Landes;Jon Williamson
客观贝叶斯认识论提出了三个准则：我们信念的强度应该是概率；它们应该根据我们的物理概率证据进行校准；否则它们应该在我们可以表达的基本命题之间充分含糊。这三个准则有时是通过诉诸最大熵原理来解释的，该原理说，信念函数应该是一个概率函数，从所有被校准为证据的函数中，具有最大熵。然而，客观贝叶斯主义的三个准则通常以不同的方式得到证明。在这篇文章中，我们证明了在最小化最坏情况的预期损失方面，这三个准则都可以归结为一个单一的理由。反过来，这相当于最大化了广义的熵概念。我们认为，除了最小化最坏情况下的预期损失之外，要求语言不变性还会促使标准熵最大化，而不是广义熵的其他实例最大化。我们的论证还为通过贝叶斯条件化更新信任度提供了一个合格的理由。然而，与贝叶斯主义的主观观点相比，条件概率在客观贝叶斯解释中扮演的核心角色并不那么重要，导致贝叶斯定理的作用减弱。
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.