标题： 带有偏斜倾向的伯努利试验用于认证和验证 显示英文标题

标题： Bernoulli Trials With Skewed Propensities for Certification and Validation

摘要： 撰写本文的动机是广受报道的媒体报告，这些报告指出波音737 Max飞机的两次事故是由于软件故障造成的。 然而，本文所考虑的问题是一个具体的问题，其旨在解决一个普遍性问题，即在大量伯努利试验全部成功的情况下，如何对药物、材料样本或复杂系统等项目进行认证以供使用。 更广泛地说，本文试图回答一个古老而崇高的哲学问题，即“仅凭经验测试能否验证自然规律？” 我们的观点是，答案取决于起始条件，即你的先验分布是什么，这个先验分布赋予了哪些未知因素，以及观察到的数据是什么。 本文是说明性的，因为它从历史回顾开始，并以一些新的想法和建议结束，以解决提出的问题。 在后续部分，它还阐述了波普尔的“倾向性”概念及其在伯努利试验下为贝叶斯推断提供适当框架的作用，以及需要处理主观指定的后验分布；也就是说，不依赖于通常的贝叶斯先验到后验的迭代。 显示英文摘要

摘要： The impetus for writing this paper are the well publicized media reports that software failure was the cause of the two recent mishaps of the Boeing 737 Max aircraft. The problem considered here though, is a specific one, in the sense that it endeavors to address the general matter of conditions under which an item such as a drug, a material specimen, or a complex, system can be certified for use based on a large number of Bernoulli trials, all successful. More broadly, the paper is an attempt to answer the old and honorable philosophical question, namely," when can empirical testing on its own validate a law of nature?" Our message is that the answer depends on what one starts with, namely, what is one's prior distribution, what unknown does this prior distribution endow, and what has been observed as data. The paper is expository in that it begins with a historical overview, and ends with some new ideas and proposals for addressing the question posed. In the sequel, it also articulates on Popper's notion of "propensity" and its role in providing a proper framework for Bayesian inference under Bernoulli trials, as well as the need to engage with posterior distributions that are subjectively specified; that is, without a recourse to the usual Bayesian prior to posterior iteration.