论文标题
作为离散时间有限国家不确定过程的全球信念模型的特定高期望
A Particular Upper Expectation as Global Belief Model for Discrete-Time Finite-State Uncertain Processes
论文作者
论文摘要
为了建模离散的有限状态不确定过程，我们主张以最高期望的形式使用全球信仰模型，该模型是一组基本公理下最保守的信仰模型。我们对这些公理的动机（描述了本地和全球信念模型应该如何相关），是基于对高期期望的两个可能的解释：类似于Walley's的行为，而对线性期望的上层信封则进行了解释。我们表明，满足我们的公理的最保守的高期望，即我们的选择模型，与Shafer和Vovk引入的特定版本的游戏理论上的高期期望相吻合。这有两个重要的含义：它可以保证有一个满足我们公理的独特全球信仰模型；它表明，Shafer和Vovk的模型可以得到公理表征，从而为采用该模型提供了另一种动机，即使在他们的游戏理论框架之外也是如此。最后，我们将模型与传统措施理论方法产生的最高期望联系起来。我们表明，这种度量理论上的期望也满足了所提出的公理，这意味着它由我们的模型或等效地是游戏理论模型主导。此外，如果所有本地模型都是精确的，则所有三个模型都重合。
To model discrete-time finite-state uncertain processes, we argue for the use of a global belief model in the form of an upper expectation that is the most conservative one under a set of basic axioms. Our motivation for these axioms, which describe how local and global belief models should be related, is based on two possible interpretations for an upper expectation: a behavioural one similar to Walley's, and an interpretation in terms of upper envelopes of linear expectations. We show that the most conservative upper expectation satisfying our axioms, that is, our model of choice, coincides with a particular version of the game-theoretic upper expectation introduced by Shafer and Vovk. This has two important implications: it guarantees that there is a unique most conservative global belief model satisfying our axioms; and it shows that Shafer and Vovk's model can be given an axiomatic characterisation and thereby provides an alternative motivation for adopting this model, even outside their game-theoretic framework. Finally, we relate our model to the upper expectation resulting from a traditional measure-theoretic approach. We show that this measure-theoretic upper expectation also satisfies the proposed axioms, which implies that it is dominated by our model or, equivalently, the game-theoretic model. Moreover, if all local models are precise, all three models coincide.
