书籍介绍

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

AI导读

核心看点

将概率论重构为逻辑推理的延伸，统一概率与统计推断。
批判频率学派，主张概率反映认知状态而非客观频率。
融合物理学直觉与数学严谨，提供贝叶斯思维的全新视角。

适合谁读

对贝叶斯统计、概率论基础及科学哲学有深入兴趣者。
具备高等数学基础，希望从本源理解数据分析原理的读者。
物理学、计算机科学及人工智能领域的研究者与从业者。

读前提醒

本书未竟且数学密集，需耐心应对逻辑与公式的频繁切换。
建议先补强微积分与线性代数基础，否则阅读体验极痛苦。
重在领悟作者将常识量化的思想，不必纠结于所有推导细节。

读者共识

被誉为贝叶斯学派圣经，思想深邃，虽晦涩但值得反复研读。
作者以物理学家直觉重构概率，对频率学派的批判极具启发性。
阅读门槛极高，常令人感到智力受挫，但精神满足感极强。

本导读基于书籍简介、目录、原文摘录、短评和书评生成，不等同于全文精读。

精彩摘录

"令A是一个数学理论背后的公理系统，T是可以从A中推导出来的任意命题或定理。现在，无论T断言什么，可以从公理推导出T的事实都不能证明公理之间没有矛盾。这是因为，即使存在矛盾，T当然也可以从这些公理中推导出来！对于我们的问题来说，这是哥德尔定理的核心思想。正如费希尔（Fisher，1956）所注意到的，它向我们展示了哥德尔的结果为什么在直觉上是正确的。我们不认为逻辑学家会接受把费希尔的简单论证作为完整的哥德尔定理的证明。然而对于我们大多数人来说，这比哥德尔冗长而复杂的论证更有说服力。"
"The writer has learned from much experience that this primary emphasis on the logic of the problem, rather than the mathematics, is necessary in the early stages. For modern students, the mathematics is the easy part; once a problem has been reduced to a definite mathematical exercise, most students"
"Good mathematicians see analogies between theorems; great mathematicians see analogies between analogies."
"How can we build a mathematical model of human common sense?"
"How could we build a machine which would carry out useful plausible reasoning, following clearly defined priciples expressing an idealized common sense?"
"Of course, on publishing a new theorem, the mathematician will try very hard to invent an argument which uses only the first kind; but the reasoning process which led to the theorem in the first place almost always involves one of the weaker forms (based, for example, on following up conjectures sug"
"Many people are fond of saying, ‘They will never make a machine to replace the human mind – it does many things which no machine could ever do.’ A beautiful answer to this was given by J. von Neumann in a talk on computers given in Princeton in 1948, which the writer was privileged to attend. In rep"
"George P´olya on ‘Mathematics and Plausible Reasoning’. He dissected our intuitive ‘common sense’ into a set of elementary qualitative desiderata. In the writer’s lectures, the emphasis was therefore on the quantitative formulation of P´olya’s viewpoint, so it could be used for general problems of s"

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