Abraham Wald and the Origins of the Sequential Probability Ratio Test

Joel B. Greenhouse and Christopher J. Phillips

The American Statistician, 2026, vol. 80, issue 1, 177-183

Abstract: Abraham Wald’s formalization of the sequential probability ratio test in the crucible of World War II is one of the more famous cases in the history of statistics of the interplay of statistical theory and real-world applications. Focusing entirely on the moments around its creation, however, obscures the way in which it was also a continuation of previous work he had done in the late 1930s, and in particular, Wald’s development of decision theory and his approach to using inverse probability. By situating the origins of the sequential probability ratio test in a broader history, we see not only how inverse probability initially made its way into sequential analysis but also the ongoing importance of the role of applications in motivating the development of statistical theory.

Date: 2026
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DOI: 10.1080/00031305.2025.2604805

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