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Inductive Logic: From Data Analysis to Experimental Design

机译：归纳逻辑：从数据分析到实验设计

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摘要

In celebration of the work of Richard Threlkeld Cox, we explore inductive logic and its role in science touching on both experimental design and analysis of experimental results. In this exploration we demonstrate that the duality between the logic of assertions and the logic of questions has important consequences. We discuss the conjecture that the relevance or bearing, b, of a question on an issue can be expressed in terms of the probabilities, p, of the assertions that answer the question via the entropy. In its application to the scientific method, the logic of questions, inductive inquiry, can be applied to design an experiment that most effectively addresses a scientific issue. This is performed by maximizing the relevance of the experimental question to the scientific issue to be resolved. It is shown that these results are related to the mutual information between the experiment and the scientific issue, and that experimental design is akin to designing a communication channel that most efficiently communicates information relevant to the scientific issue to the experimenter. Application of the logic of assertions, inductive inference (Bayesian inference) completes the experimental process by allowing the researcher to make inferences based on the information obtained from the experiment.
机译：为庆祝Richard Threlkeld Cox的工作，我们探索归纳逻辑及其在科学中的作用，涉及实验设计和实验结果分析。在这个探索中，我们证明断言逻辑和问题逻辑之间的对偶具有重要的后果。我们讨论这样一个猜想：一个问题与一个问题的相关性或方位b可以用通过熵回答该问题的断言的概率p来表示。在将其应用于科学方法时，可以将问题的逻辑（归纳性探究）应用于设计最有效解决科学问题的实验。这是通过最大程度地提高实验问题与要解决的科学问题的相关性来执行的。结果表明，这些结果与实验和科学问题之间的相互信息有关，并且实验设计类似于设计一种最有效地将与科学问题有关的信息传达给实验者的交流渠道。运用断言逻辑，归纳推理（贝叶斯推理）通过允许研究人员根据从实验中获得的信息进行推理来完成实验过程。

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