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首页> 外文期刊>Artificial intelligence >Imprecise probability trees: Bridging two theories of imprecise probability
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Imprecise probability trees: Bridging two theories of imprecise probability

机译：不精确概率树：桥接两个不精确概率理论

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摘要

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of probability trees and random processes in the framework of Walley's theory. We indicate how our results can be used to reduce the computational complexity of dealing with imprecision in probability trees, and we prove an interesting and quite general version of the weak law of large numbers.
机译：我们对概率论的两种方法进行了概述，其中使用了上下概率而不是概率：沃尔利的不精确概率行为理论，以及谢弗和沃夫克对概率的博弈论解释。我们证明了这两种理论比一见钟情更紧密地联系在一起，并且我们在它们之间建立了一种对应关系：（i）具有有趣的解释，并且（ii）允许我们将一种理论的结果自由地导入另一种理论中。我们的方法导致了在Walley理论框架内对概率树和随机过程的解释。我们指出了如何使用我们的结果来降低处理概率树中不精确性的计算复杂性，并且证明了大数弱定律的有趣且相当通用的版本。

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