This paper is about two things: (i) Charles Sanders Peirce (1837-1914) -- an iconoclastic philosopher and polymath who is among the greatest of American minds. (ii) Abductive inference -- a term coined by C. S. Peirce, which he defined as "the process of forming explanatory hypotheses. It is the only logical operation which introduces any new idea." Abductive inference and quantitative economics: Abductive inference plays a fundamental role in empirical scientific research as a tool for discovery and data analysis. Heckman and Singer (2017) strongly advocated "Economists should abduct." Arnold Zellner (2007) stressed that "much greater emphasis on reductive [abductive] inference in teaching econometrics, statistics, and economics would be desirable." But currently, there are no established theory or practical tools that can allow an empirical analyst to abduct. This paper attempts to fill this gap by introducing new principles and concrete procedures to the Economics and Statistics community. I termed the proposed approach as Abductive Inference Machine (AIM). The historical Peirce's experiment: In 1872, Peirce conducted a series of experiments to determine the distribution of response times to an auditory stimulus, which is widely regarded as one of the most significant statistical investigations in the history of nineteenth-century American mathematical research (Stigler, 1978). On the 150th anniversary of this historical experiment, we look back at the Peircean-style abductive inference through a modern statistical lens. Using Peirce's data, it is shown how empirical analysts can abduct in a systematic and automated manner using AIM.

翻译：本文涉及两个主题：(i) 查尔斯·桑德斯·皮尔士（1837-1914）——一位打破传统、博学多识的哲学家，堪称美国最伟大的思想家之一；(ii) 溯因推理——由C.S.皮尔士提出的术语，他将其定义为“形成解释性假说的过程，是唯一能够引入新思想的逻辑操作”。溯因推理与数量经济学：溯因推理作为发现与数据分析工具，在实证科学研究中扮演着基础性角色。Heckman与Singer（2017）强烈主张“经济学家应进行溯因推理”。Arnold Zellner（2007）强调，“在计量经济学、统计学和经济学的教学中，应大幅增加对还原[溯因]推理的重视”。但目前尚无成熟的理论或实用工具能让实证分析师进行溯因推理。本文通过向经济学与统计学界引入新原理与具体操作步骤，尝试填补这一空白。我将所提出方法命名为“溯因推理机”（AIM）。历史性皮尔士实验：1872年，皮尔士进行了一系列实验，用于确定听觉刺激的反应时间分布，这被广泛视为19世纪美国数学研究史上最重要的统计调查之一（Stigler, 1978）。在这一历史性实验150周年之际，我们以现代统计视角回顾皮尔士式的溯因推理。利用皮尔士的数据，本文展示了实证分析师如何通过AIM实现系统化、自动化的溯因推理。