Virginia Tech's Irving John (Jack) Good, one of the founders of modern Bayesian inference and a member of the World War II code-breaking team at Bletchley Park, died of natural causes on April 5 in Radford, Va. He was 92.

A citizen of the United Kingdom, Good was professor of statistics in the College of Science since 1967. In 1969 he was appointed University Distinguished Professor, and attained emeritus status in 1994.

He also held adjunct professorships at Virginia Tech in the Center for the Study of Science in Society and the Department of Philosophy. Before coming to Virginia Tech, he had worked for British Military Intelligence in the Government Communications Headquarters specializing in signals intelligence. Among other government, academic, and consulting positions, he also held faculty positions at the University of Manchester and at Oxford University.

Good made fundamental contributions to the theory of Bayesian inference, drawing in part on ideas he developed while working to break the German Enigma code during World War II. He worked at Bletchley Park in Hut 8 with Alan Turing, Hugh Alexander, and Max Newman, where he was also deeply involved in the early development of computing.

In particular, the Bletchley Park scientists built the “Heath Robinson” (named after the English Rube Goldberg), a very early computer, in order to break one of the German encryption systems. That machine used vacuum tubes, was highly unreliable, and thus required extensive statistical work, largely by Good and his long-time friend, the well-known artificial-intelligence pioneer Donald Michie.

After the war, Good went with Alan Turing to the University of Manchester to work with M. H. A. Newman on statistical and mathematical computing, but was soon asked to rejoin British intelligence. Much of the work that he did there is still classified, but in his spare hours he began to systematically develop Bayesian statistics and the theory of the “weight of evidence”. At the time, Bayesian statistics was not popular. Other methods, primarily frequentist methods, were dominant, and that dominance persisted until the early 1990s.

But Good’s work (along with that of other early Bayesians, notably Harold Jeffreys, Dennis Lindley, and Leonard Jimmie Savage) was instrumental in shifting the balance. His particular contributions were to the theory of Bayesian inference for two-way tables, the use of weight of evidence as a concept for hypothesis testing, the philosophical examination of the foundations of statistical inference, and the invention of penalized likelihood as a criterion for estimation (this has now become an almost universal tool in data mining and other complex analyses).

His major books included *Probability and the Weighing of Evidence* (1950), *The Estimation of Probabilities: an Essay on Modern Bayesian Methods* (1965), and *Good Thinking: the Foundations of Probability and its Applications* (1983). His short list of publications, and other information are available online.

Good was educated in mathematics at Cambridge University where he was awarded a Smith’s Prize (1940) under A. S. Besicovitch, F.R.S., a Ph.D. (1941) under the eminent G. H. Hardy, an Sc. D. (1963), and a D. Sc. (1964) from Oxford.

He particularly loved combinatorics and number theory. A fan of numerology, he liked to point out that he arrived in Blacksburg on the seventh hour of the seventh day of the seventh month of the seventh decade of the seventh year and was put in apartment seven of the seventh block of Terrace View Apartments, all by chance. Over the course of a long career he discovered hundreds of combinatorial identities, usually in connection with functions of well-known statistical distributions.

Good’s work had great breadth, spanning statistics, computation, number theory, and philosophy. His method for the fast calculation of discrete Fourier transforms, published in 1958, inspired Tukey and Cooley’s work on the Fast Fourier Transform. In 1967, he went to Hollywood briefly to advise Stanley Kubrick on scientific issues related to filming 2001: A Space Odyssey.

While at Virginia Tech, he published a significant number of papers in statistics, physics, mathematics and philosophy. He was also fond of shorter articles and became the editor of “Comments, Conjectures, and Conclusions” for the Journal of Statistical Computation and Simulation. A collection of his shorter notes was recently published by Rice University Press in 2009. Although he did not teach many classes or have many Ph.D. students, he was tremendously supportive of the research of students and faculty at Virginia Tech and the broader scientific community, leading to many joint publications.

Born Dec. 9, 1916 in London to Polish-Jewish immigrants, he was given the name Isidore Jacob, which he later changed to Irving John He was a child prodigy, independently discovering logarithms, the irrationality of the square root of two, and proof by induction at about the age of 9.

Good, who remained single throughout his life, was preceded in death by his father, Morris Edward Good (known in Yiddish literary circles as Moshe Oved), his mother Sophia Polikoff Good, a sister Sylvia and a brother Arthur. He is survived by a half-sister Yemaiel Aris, nephews Raymond and Desmond Good, and their families of England, cousin James Randall of New York City, other relatives, devoted personal friend Leslie Pendleton and other close friends in the Blacksburg area as well as the academic statistical community.

A memorial service will be held at 2 p.m. Sunday, April 19, at the Blacksburg Jewish Community Center, corner of Church and Roanoke Streets, Blacksburg, Va. Those who wish to honor him with a charitable donation may consider the Elie Wiesel Foundation for Humanity in memory of I. J. Good.