As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework.

中文翻译：

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贝叶斯决策理论和随机独立性

由于随机独立性对于概率论的数学发展至关重要，因此任何关于概率的基础工作似乎都应该能够解释这一特性。贝叶斯决策理论在这方面似乎很欠缺。萨维奇关于不确定性下偏好的假设需要主观预期效用表示，这仅断言主观概率测度的存在和唯一性，而不管其属性如何。缺少的是对应于随机独立性的偏好条件。为了填补这一重大空白，本文重新公理化了贝叶斯决策理论，并证明了这个新框架中的几个表示定理。