Colin Lingwood Mallows, with his wife Jean

Colin Lingwood Mallows was born on September 10, 1930, in Great Sampford, a small village in Essex, England. His father was the village policeman, who later became Chief Inspector at the police headquarters in Chelmsford, responsible for education and record-keeping with regard to road safety. In this role his father developed some new statistical procedures, so perhaps this sparked Colin’s interest.

In 1940, at the beginning of the Battle of Britain, Mallows’ parents evacuated Colin and his brother to Cape Town, South Africa. He returned to England in 1945 and in 1948 began studying at University College London, in the Department of Mathematics. He soon moved to the Department of Statistics, founded by Karl Pearson in 1911 as the first ever statistics department and where modern statistics began. When Mallows began his studies, Egon Pearson was the Professor and the faculty included F.N. David, N.L. Johnson, and H.O. Hartley. Colin finished his PhD in 1953 under David and Johnson and all four parts of his thesis were published. For the following two years he served his National Service in the Royal Artillery.

While at University College, he met his wife Jean at a local dance in Essex, and the first thing he asked her, while the lights were getting dimmed, was whether she could trust him in the dark. The rest was history. Colin and Jean married in 1956 and continued folk dancing for many years.

Following his graduation, in quick succession followed one year at University College London, another year at Princeton University where John Tukey recruited him, and another two years at University College. Finally, in 1960 he joined Bell Labs, in Murray Hill, New Jersey. He felt that he had, as he put it, “lucked into the best job in the world” with early colleagues like John Tukey, Brad Murphy, Martin Wilk, Ram Gnanadesikan, Bill Williams, Dave Brillinger and Frank Anscombe. He really enjoyed the stimulating environment of Bell Labs. Contributing factors were that the management was highly technical and allowed researchers to explore new directions without constraints, combined with the presence of a constant stream of new problems and collaborations with colleagues in engineering and the mathematical, physical and social sciences. He was greatly influenced by John Tukey’s path-breaking work on data analysis and invention of statistical tools such as box plots and stem-and-leaf diagrams. For years Colin taught data analysis courses based on these and other ideas at Bell Labs.

Later the statistical effort grew, and he and Ram Gnanadesikan became department heads at Bell Labs and recruited John Chambers, Siddhartha Dalal, Trevor Hastie, Jon Kettenring, Jim Landwehr, Vijay Nair, Yehuda Vardi and others. In 1995, at one more breakup of AT&T, he joined AT&T Labs, from which he formally retired in 2000 and then began consulting at Avaya Labs (a second-generation spin-off from AT&T).

Colin Mallows was a prolific researcher and wrote over 200 papers and several research notes, and was a co-inventor on five patents. He is probably most well known for inventing, with stimulation from Cuthbert Daniels, what came to be known as “Mallows C_p Statistic,” a regression model diagnostic procedure which is still used every day around the world. He personally felt that C_p should be used only as a descriptive tool to assess whether a set of variables was as good as another one, and that min C_p should not be used as a criterion.

“A Conversation with Colin L. Mallows” was published in the International Statistical Review in December, 2013 (vol. 81(3), pp. 338–360; https://www.jstor.org/stable/43299641). In this conversation Mallows described his approach to statistical problems, the Bell Labs research environment and how it appealed to him and enabled him to thrive, his work on AT&T regulation issues, how he approached research and mathematical problems in general, and other topics.

Besides C_p, he worked on rank models, regression diagnostics, network engineering, software engineering, stopping rules, inequalities, order statistics, robust statistics, smoothing, experimental designs, software testing, matrix methods, principles of data analysis, implementation of governmental regulations, privacy and security, coding theory, combinatorics, Apollonian packing and other topics with numerous colleagues across the world. Some of the problems were purely mathematical, though his approach was unique in that he always tried to think of relevant data which would give him insight into deeper mathematical arguments. A classic example of this was in the context of a challenging problem with a major prize posed by a famed mathematician, John Conway, on Conway Sequences. Colin solved the problem with his unique insights from data analysis and simulations.

He felt that statisticians were spending comparatively little time on the so-called “Zero^th problem”—the first problem being the formation of specifications for the data; the second being design procedures for dealing with data that makes sense in context of the specification; and the third problem being distributional aspects and inference. Before all these, the “Zero^th problem” involves how one thinks about what data ought to be collected for the problem at hand. He wove these ideas into his COPSS Fisher Lecture at the 1997 Joint Statistical Meetings.

He always believed in looking at data before making any assumptions. Thus, he felt uncomfortable with Bayesian assumptions on prior distributions as well as truly believing the distributional model. Nevertheless, he often approached problems from a Bayesian perspective to identify a method of analysis and later on would question its assumptions.

He felt that statistics was similar to engineering, in that in engineering one has to deal with the real world—a bridge either stands up or it doesn’t. In statistics, the procedure either makes sense and helps with the real problems or it doesn’t. He felt that the statistics profession has opportunities everywhere, but it has sometimes been unwilling to take the lead on new emerging areas such as machine learning. Another concern he had was how best to teach applied statistics in the classroom.

Colin was a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the Royal Statistical Society. As well as the Fisher Lecture in 1997, he was the ASA Deming Lecturer in 2004, and received the Wilks Memorial Award in 2007. He also received the AT&T Science and Technology medal in 1999.

Colin stayed interested and engaged in research until his final days. In the summer of 2023 he was approached by a psychologist researcher from many years ago in their Bell Labs days about reviving and revising a technical memorandum they had written and distributed internally at Bell Labs but never published. The revision was completed in August, with the most important change being the addition of some data—the original memorandum was purely theoretical. It is currently under review at a psychological journal.

One of his main hobbies was table tennis—he played in a league at a club in Westfield, New Jersey, at least one night a week for over fifty years. He competed well into his 80s. Another pleasure was writing limericks for special occasions. Colin and his wife owned a 70-acre farm in northwestern New Jersey for about 20 years. It was heavily wooded and they raised sheep. Colin fixed fences and really enjoyed cutting down trees.

Colin Mallows died on November 4, 2023, aged 93. He is survived by his wife of 67 years, Jean, three daughters, eight grandchildren, fourteen great-grandchildren; and one great-great grandson.

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By Siddhartha Dalal and James Landwehr

Colin Mallows’ Key Publications by Areas of Research:

Combinatorics: Mallows, C.L. and Wachter, K.W. Valency enumeration of rooted plane trees J. Australian Math. Soc.13, 472–476. (1972).

Covering designs: Dalal, S.R. and Mallows, C.L. Factor-covering designs for testing software Technometrics 40, 234–243. (1998).

Inequalities: Mallows, C.L. and Richter, D. Inequalities of Chebychev type involving conditional expectations Ann. Math. Statist. 40, 1922–1932. (1969).

Probability: Mallows, C. 1. A note on asymptotic joint normality Ann. Math. Statist. 43, 508–515. (1972); Mallows, C.L. Sequential sampling of finite populations with and without replacement SIAM J. Appl. Math. 24, 164–168. (1973); Chambers, J.M., Mallows, C.L. and Stuck, B.W. A method for simulating stable random variables JASA 71, 340–344. (1976); Mallows, C.L. and Shepp, L.A. B–stability J. Appl. Probab. 42, 581–586 (2005).

Ranking: Mallows, C.L. Non-null ranking models, I Biometrika 44, 114–130. (1957).

Robustness: Denby, L. and Mallows, C.L. Two diagnostic displays for robust regression analysis Technometrics 19, .1–13. (1977); Hajek, Hoeffding, Tukey, and Von Mises, Summary of talks at Princeton, May 10, 1971.

Smoothing: Mallows, C.L. Some theoretical results on Tukey’s 3R smoother in Smoothing Techniques for Curve Estimation Lecture Notes #757, 77–90. Springer-Verlag. (1979); Mallows, C.L. Some theory of nonlinear smoothers Ann. Statist. 8, 695–715. (1980).

Applications: Denby, L. Landwehr, J.M. and Mallows, C.L. An exercise in the real world of design and analysis The American Statistician 55, 263–271 (2001); Mallows, C.L. Parity: Implementing the Telecommunications Act of 1996 Statistical Science 17, 256–270. (With discussion, 271–285). (2002).

Foundation: Mallows, C.L. and Walley, P. A theory of data analysis? Pmc. Bus. and Econ. Stat. Sec., ASA (1980); Draper, D.R, Hodges, J.S., Mallows, C.L. and Pregibon, D. Exchangeability and data analysis J. Roy. Statist. Soc. Ser. A 156, 9–28 (with discussion, 28–37) (1993); Mallows, C.L. The zero^th problem The American Statistician 52, 1–9. (1998).

Statistical Math: Mallows, C.L. and Wachter, K.W. The asymptotic configuration of Wishart eigenvalues (abstract) Ann. Math. Statist. 61 p. 1384 (1970); Denby, L. and Mallows, C.L. Singular values of large matrices subject to Gaussian perturbation Proc. 23rd Symp. Interface, 54–57. (1991).

Methods: Mallows, C.L. Latent vectors of random symmetric matrices Biometrika 48, 133–149. (1961); Williams, W.H. and Mallows, C.L. The potential systematic behavior of some panel survey estimates Proc. Soc. Stat. Sect., ASA, 44–54. (1969); Mallows, C.L. Some comments on C_p Technometrics 15, 661–667. (1973) (Reprinted in Technometrics 42, .87–94 (2000), with introduction by R.F. Gunst, 62–64); Mallows, C.L. Augmented partial residuals Technometrics 28, 313–319. (1986); Cleveland, W.S., Mallows, C.L. and McRae, J.E. ATS methods: nonparametric regression for non-Gaussian data JASA 88, 821–835. (1993); Mallows, C.L., More Comments on C_p Technometrics 37, 362–372 (1995); Denby, L. and Mallows, C.L. Variations on the histogram J Comp. and Graph. Statist. 18, 21–31 (2009).

Stopping: Dalal, S.R. and Mallows, C.L. When should one stop testing software? JASA 83, 872–879. (1988); Dalal, S.R and Mallows, C.L. Buying with exact confidence Ann. Appl. Prob. 2, 752–765. (1992)