The scientific process is a means to turn the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific process in a precise mathematical language. This paper outlines one such language. What is presented here is hardly new. The material is based on great thinkers from times past well as more modern contributions. The novel contributions of this paper are: A new general data processing inequality, a bias variance decomposition for canonical losses, streamlined proofs of the Blackwell-Sherman-Stein and Randomization theorems. means of calculating deficiency through linear programming.
翻译:科学过程是将实验结果转化为关于我们所处世界的知识的一种手段。大量研究工作致力于实现这一过程的自动化。为此,需要以精确的数学语言来表述科学过程。本文概述了这样一种语言。这里所呈现的内容并非全新,其材料基于过往伟大思想家以及更现代的贡献。本文的新颖贡献在于:一种新的通用数据处理不等式、规范损失的偏差-方差分解、Blackwell-Sherman-Stein定理与随机化定理的简化证明,以及通过线性规划计算缺陷的方法。