A Conversation with James Hannan

Abstract

Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeated games was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II, Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play that apply to selecting the best forecaster.

James Hannan was born in Holyoke, Massachusetts on September 14, 1922. He attended St. Jerome’s High School and in January 1943 received the Ph.B. from St. Michael’s College in Colchester, Vermont. Jim enlisted in the US Army Air Force to train and serve as a meteorologist. This took him to army airbases in China by the close of the war. Following discharge from the army, Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To prepare for doctoral work in statistics at the University of North Carolina that fall, Jim went to the University of Michigan in the summer of 1947. The routine admissions’ physical revealed a spot on the lung and the possibility of tuberculosis. This caused Jim to stay at Ann Arbor through the fall of 1947 and then at a Veterans Administration Hospital in Framingham, Massachusetts to have his condition followed more closely. He was discharged from the hospital in the spring and started his study at Chapel Hill in the fall of 1948. There he began research in compound decision theory under Herbert Robbins. Feeling the need for teaching experience, Jim left Chapel Hill after two years and short of thesis to take a three year appointment as an instructor at Catholic University in Washington, DC. When told that renewal was not coming, Jim felt pressure to finish his degree. His 1953 UNC thesis contains results in compound decision theory, a density central limit theorem for the generalized binomial and exact and asymptotic distributions associated with a Kolmogorov statistic. He was encouraged to apply to the Department of Mathematics at Michigan State University and came as assistant professor in the fall of 1953. In the next few years, he accomplished his work on repeated games. The significance of the work was rediscovered by the on-line learning communities in computer science in the 1990s and the term Hannan consistency was coined. His retirement came in 2002 after a long career that included major contributions to compound and empirical Bayes decision theory and other areas. He and his colleague Václav Fabian co-authored Introduction to Probability and Mathematical Statistics (Wiley 1985).

A Hannan strategy is a strategy for the repeated play of a game that at each stage i plays a smoothed version of a component Bayes rule versus the empirical distribution Gi-1 of opponent’s past plays. [Play against the unsmoothed version is often called (one-sided) fictitious play.] As in compound decision theory, performance is measured in terms of modified regret, that is, excess of average risk across stages i=1, …, n over the component game Bayes envelope R evaluated at Gn. Hannan, James F., Approximation to Bayes Risk in Repeated Play, Contributions to the Theory of Games 3 97–139, Princeton University Press, is a paper rich with bounds on modified regrets. A Hannan consistent strategy is one where limsup (modified regret) is not greater than zero. In the 1990s, greater recognition of Hannan’s work began to emerge; the term Hannan consistency may have first appeared in Hart and Mas-Colell [J. Econom. Theory 98 (2001) 26–54].

Early on, only his students and a few others were aware of the specifics of his findings. The failure of others to recognize the specific results in the 1957 paper may be due to the cryptic writing style and notation of the author. The strategy for selecting forecasters in Foster and Vohra [8] [Operations Research 41 (1993) 704–709] is an unrecognized Hannan-strategy as is the strategy in Feder et al. [7] [IEEE Trans. Inform. Theory 38 (1992) 1258–1270]. Gina Kolata’s New York Times article, “Pity the Scientist who Discovers the Discovered” (February 5, 2006) uses the original Hannan discoveries as an example, although referring to him as a “statistician named James Hanna.”

In May 1998, the Department of Statistics and Probability hosted a Research Meeting in Mathematical Statistics in Honor of Professor James Hannan. Many came to honor Jim; the speakers included Václav Fabian, Stephen Vardeman, Suman Majumdar, Richard Dudley, Yoav Freund, Dean Foster, Rafail Khasminskii, Herman Chernoff, Michael Woodroofe, Somnath Datta, Anton Schick and Valentin Petrov.

Jim was ever generous in giving help to students. He enjoyed improving results and was very reluctant to submit research results until much effort was made to improve them. Jim directed or co-directed the doctoral research of twenty students: William Harkness (1958), Shashikala Sukatme (1960), John Van Ryzin (1964), Dennis Gilliland (1966), David Macky (1966), Richard Fox (1968), Allen Oaten (1969), Jin Huang (1970), Vyagherswarudu Susarla (1970), Benito Yu (1971), Radhey Singh (1974), Yoshiko Nogami (1975), Stephen Vardeman (1975), Somnath Datta (1988), Jagadish Gogate (1989), Chitra Gunawardena (1989), Mostafa Mashayekhi (1990), Suman Majumdar (1992), Jin Zhu (1992) and Zhihui Liu (1997). Most pursued academic careers and some ended up at research universities including Pennsylvania State, Columbia, Michigan State, UC-Santa Barbara, Guelph, SUNY-Binghamton, Iowa State, Louisville, Nebraska-Lincoln and Connecticut-Stamford.

It was in the Army in 1944 that Jim read his first statistics book. It was War Department Education Manual EM 327, An Introduction to Statistical Analysis, by C. H. Richardson, Professor of Mathematics, Bucknell University, published by United States Armed Forces Institute, Madison, Wisconsin (CQ).