William Rae Thompson

William Rae Thompson was an American mathematician and researcher who made foundational contributions to statistics and probability theory. He is best known as the original creator of Thompson sampling, a heuristic algorithm that has become a cornerstone of modern artificial intelligence, machine learning, and clinical trial design.Thompson, William R. (1933). "On the Likelihood that One Unknown Probability Exceeds Another in View of the Evidence of Two Samples". Biometrika. 25 (3/4): 285–294. doi:10.1093/biomet/25.3-4.285.

Early life and education

Thompson completed his undergraduate studies at Columbia University, earning a Bachelor of Arts (B.A.) degree in 1923.Historical Register of Yale University, 1701-1937. Yale University. Search this book on He later attended Yale University, where he earned his Ph.D. in 1930. His doctoral dissertation, held by the Yale University Archives and the Beinecke Library, was titled On The Possible Forms Of Discriminants Of Algebraic Fields.Thompson, William R. (1930). On The Possible Forms Of Discriminants Of Algebraic Fields (Ph.D. thesis). Yale University. This work was subsequently published in parts in the American Journal of Mathematics in 1931 and 1933.Thompson, William R. (1931). "On the Possible Forms of Discriminants of Algebraic Fields I". American Journal of Mathematics. 53 (1): 81–90. doi:10.2307/2370868.

Academic career at Yale

Thompson was officially affiliated with Yale University from 1924 to 1936. Despite his mathematical background, he spent a significant portion of his career working as a researcher within the Yale Department of Pathology. His academic appointments in the department included:

Research Assistant in Pathology (Instructor rank), from 1928 to 1934.
Research Assistant in Pathology (Assistant Professor rank), from 1934 to 1936.

During his time at Yale, Thompson's tenure overlapped with Milton Winternitz, who served as the Brady Professor of Pathology, Chair of the Department, and Dean of the Medical School.Spiro, Howard (2003). "Dean Milton C. Winternitz at Yale". Perspectives in Biology and Medicine. 46 (3): 403–412. doi:10.1353/pbm.2003.0046. PMID 12878810.

Publications and Thompson sampling

Thompson was an active researcher during his years at Yale, with his articles appearing in the compiled departmental records beginning in 1931.Collected published articles from the Department of Pathology (Volumes 1-3, 1933-1939). Harvey Cushing/John Hay Whitney Medical Library, Yale University. Search this book on His research spanned diverse disciplines, applying mathematical and geometric principles to biology. His studies included respirometry, the effects of radiation on biological systems, and the geometric properties of microscopic configurations. He frequently collaborated with Yale colleagues such as R. Tennant, R. Hussey, and D. M. Grayzel.

The interdisciplinary nature of his work was reflected in his publications. In September 1933, he co-authored a paper in the journal Science concerning the anatomical properties of the pancreas across different species.Thompson, W. R.; Tennant, R.; Hussey, R. (September 22, 1933). "Frequency-Distribution of Volume of Islands of Langerhans in the Pancreas of Man, Monkey and Dog". Science. 78 (2021): 270. doi:10.1126/science.78.2021.270-a.

His most significant contribution to the fields of statistics and machine learning was published a few months later in December 1933. The paper, titled "On the Likelihood That One Unknown Probability Exceeds Another in View of the Evidence of Two Samples," was published in Biometrika (Volume 25, parts 3 and 4, pages 285–294). This work formally introduced the probability matching algorithm now known as Thompson sampling.

Legacy

Despite the long-lasting impact of Thompson sampling on modern computing and reinforcement learning (particularly in multi-armed bandit problems), William Rae Thompson lacked a dedicated biography for many years. Historically, some online resources and encyclopedias confused his identity with that of his contemporary, the Canadian entomologist William Robin Thompson, who published under the same initials. Recent clarifications of archival records from the Yale School of Medicine have helped to correctly attribute this foundational mathematical framework to William Rae Thompson's work in the pathology department.

Selected publications

Thompson, William R. (1931). "On the Possible Forms of Discriminants of Algebraic Fields I". American Journal of Mathematics. 53: 81–90. doi:10.2307/2370868.
Thompson, William R.; Hussey, Raymond (September 20, 1931). "The Effect of Radiations from a Mercury Arc in Quartz on Enzymes. II. The Effect of Ultra-Violet Radiation on Amylase in Solution". Journal of General Physiology. 15 (1): 9–13. doi:10.1085/jgp.15.1.9. PMC 2141147.
Thompson, William R. (May 1932). "The Geometric Properties of Microscopic Configurations. I. General Aspects of Projectometry". Biometrika. 24 (1/2): 21–26. doi:10.1093/biomet/24.1-2.21.
Thompson, W. R.; Tennant, R.; Hussey, R. (September 22, 1933). "Frequency-Distribution of Volume of Islands of Langerhans in the Pancreas of Man, Monkey and Dog". Science. 78 (2021): 270. doi:10.1126/science.78.2021.270-a.
Thompson, William R. (December 1933). "On the Likelihood That One Unknown Probability Exceeds Another in View of the Evidence of Two Samples". Biometrika. 25 (3/4): 285–294. doi:10.1093/biomet/25.3-4.285.

References

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