最大熵：推理的通用方法
Maximum Entropy: The Universal Method for Inference
摘要：
在这篇论文中，我们首先提供一些细节，关于我们如何达到我们目前的理解概率和我们如何操纵他们-产品和加法规则考克斯。我们还讨论了熵的现代观点，以及它如何与已知的熵，如热力学熵和信息熵。接下来，我们表明，斯奇林的方法诱导我们一个独特的一般理论归纳推理，ME方法，正是它是如何，其他熵，如雷尼或Tsallis排除的问题的推理。然后，我们探讨贝叶斯和ME更新的兼容性。我们表明，ME是能够生产的每一个方面的正统贝叶斯推断，并证明了贝叶斯和熵方法的完全兼容性。ME方法将贝叶斯规则作为一种特殊情况，这一认识使我们能够超越贝叶斯规则，同时处理数据和期望值约束。我们讨论了一般问题的非交换约束，当他们应该被顺序处理时，同时。一般的“规范”形式的后验分布的问题，同时更新的数据和时刻。这是一项重大成就，因为它表明ME不仅能够处理约束形式的信息，如MaxEnt和数据形式的信息，如贝叶斯定理，而且还可以同时处理这两种形式，这是贝叶斯和MaxEnt无法单独完成的。最后，我们说明了这种新方法的一些潜在的应用，通过应用ME潜在的问题的兴趣。
英文摘要：
In this thesis we start by providing some detail regarding how we arrived at our present understanding of probabilities and how we manipulate them - the product and addition rules by Cox. We also discuss the modern view of entropy and how it relates to known entropies such as the thermodynamic entropy and the information entropy. Next, we show that Skilling's method of induction leads us to a unique general theory of inductive inference, the ME method and precisely how it is that other entropies such as those of Renyi or Tsallis are ruled out for problems of inference. We then explore the compatibility of Bayes and ME updating. We show that ME is capable of producing every aspect of orthodox Bayesian inference and proves the complete compatibility of Bayesian and entropy methods. The realization that the ME method incorporates Bayes' rule as a special case allows us to go beyond Bayes' rule and to process both data and expected value constraints simultaneously. We discuss the general problem of non-commuting constraints, when they should be processed sequentially and when simultaneously. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and moments is obtained. This is a major achievement since it shows that ME is not only capable of processing information in the form of constraints, like MaxEnt and information in the form of data, as in Bayes' Theorem, but also can process both forms simultaneously, which Bayes and MaxEnt cannot do alone. Finally, we illustrate some potential applications for this new method by applying ME to potential problems of interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
