Michael Arthur Stephens, 1927–2019

Michael Arthur Stephens, born April 26th, 1927, died on April 10th, 2019, at the age of 91 years. He made seminal contributions to directional data and to goodness of fit and played an important role in the development of the Statistical Society of Canada. More than that, Michael educated, and entertained, generations of young statisticians. Michael was born and raised in Bristol, England. His parents were divorced when Michael was quite young and his mother disappeared from his life. He then lived for some time with his grandmother and grandfather (a bookie), his father having moved to Southampton before being killed in the Blitz in 1941. Michael took the long way round to statistics. At the age of 11 years he won a scholarship to Queen Elizabeth Hospital, a Bristol boarding school dating from 1590 where he eventually became ‘head boy’ and enjoyed a successful rugby career to go with his successful academic career. The result was a scholarship to Bristol University where he obtained a physics Honours degree in 1948 before going to Harvard University as the first holder of the Frank Knox Scholarship; he completed his Artium Magister degree in physics there in 1949. It was at this point that Michael decided to switch to mathematics, teaching for the next 10 years. Only in 1959, at age 32 years, did Michael switch to statistics, starting his doctorate at the University of Toronto under the supervision of Geoffrey Watson. In 1962 Michael graduated, married his wife, Evelyne, and published his first three papers, all in Biometrika. He saw it as a very good year indeed. He stayed on at Toronto to teach but then found a tenure track job at McGill University where he started in 1963. He was appointed Professor at Nottingham in 1970 but left for McMaster University in Hamilton, Canada, 2 years later. In 1976 he moved to Simon Fraser University, becoming Emeritus Professor there in 1992. Along the way, Michael and Evelyne had a daughter, Madeleine, who is now herself married with four sons of whom Michael was very proud indeed. It was Geoff Watson who introduced Michael to directional data for his doctoral thesis and it was Geoff's introduction of the goodness-of-fit statistic U2, for data on the circle, that led Michael to the whole area of goodness of fit. These two topics occupied most of Michael's career. By the time he went to Nottingham he had 16 papers in Biometrika, two in the Annals of Statistics, two in the Journal of the Royal Statistical Society, Series B, and two in the Journal of the AmericanStatistical Association—a remarkable start to a career. If you read Michael's papers you will see that he wrote smoothly and flowingly; he edited his work assiduously. For much of the time before he retired that meant literally cutting and pasting as he took a draft, cut it into pieces, taped them into new places and inserted scrawls that only Sylvia Holmes could read. This focus on the writing derived from a dedication to marrying theory to practice and ensuring that readers could duplicate the analyses that he suggested without any intervening confusion. Michael was an early adopter of computing. He learned Fortran at Case Western University in 1956 and continued writing and running Fortran code until he died. He used to speak with pride of having earned $100 (Canadian) while a doctoral student by producing code for a chemist who needed to evaluate some complex-valued functions. He leaves behind thousands of Fortran programs; I wish that I could tell you that they were carefully documented. We often laughed at the orphaned pieces of code that would be left behind as he edited the code—still in the file but in such a way that they could never be executed. This was still the age of statistical tables and Michael worked on several for Egon Pearson that appeared in the Biometrika Tables. Indeed Michael collaborated over many years with Pearson on a variety of topics. Pearson's request for smaller tables, for instance, led Michael to produce ‘modified’ goodness-of-fit statistics; a sample-size-dependent location–scale shift of the original statistic for which the convergence of the null distribution to the asymptote was very fast. Pearson also introduced Michael to the use of Pearson curves; the four-parameter family, introduced by Pearson's father, Karl, that includes so many of the famous distributions of statistics. Michael used his original code (which really just interpolated in a table) for many years and was always happy when he could compute the first four moments of a statistic so that he could fit another Pearson curve. Michael's most influential work was in goodness of fit; he was proudest of the 1986 book Goodness-of-fit Techniques which he co-edited with Ralph D’Agostino. He wrote four chapters in that book himself and I know that they were a labour of love. The book focuses sharply on practice, not theory; Michael himself was fond of asking ‘what would the practical man want?’. In particular, of course, Michael was the leading proponent of three quadratic empirical distribution function tests—the Cramér–von Mises, Anderson–Darling and Watson's tests. These tests of the hypothesis that a sample has some distribution have themselves distributions which depend on whether or not any parameters are estimated, on the family of distributions in question, and in general on the specific parameter value. The distributions are those of a sum of weighted χ2-variates and the weights are found by solving a (Fredholm) integral equation. Michael loved the related special function theory; he and I spent many hours solving the equivalent boundary value ordinary differential equation problems. Michael worked with many people over his career. Along the way he built many friendships. Michael listened to those friends—listened and remembered. He empathized, and then, when you met again, he would follow up, ask after your family, remember anything which might previously have been troubling you. This made him a great friend but also one of the all-time great story tellers. He was a very popular after-dinner speaker, delivering off-the-cuff remarks that he had practised for hours in front of a mirror. He would poke gentle fun (sometimes, I confess, with a bit of bite) but always with good humour and good intentions. Michael had stories of the theatre in which he took a deep, life-long interest. He had stories of his rugby career at school in Bristol, of the other boys at his school and where they ended up in life, and of his political interests (in the UK Liberal Party of the day). He told stories of people whom he met at Harvard, at Case Western, in France, of Evelyne and her family's war experiences and of his in-laws. He told stories of his time teaching engineering students in Battersea Polytechnic in London while sharing an office with one of the Polish code-breakers whose work was an essential part of the breaking of the Enigma code. He told vivid stories with great detail on these and many, many more topics. I shall miss these stories but more importantly I miss Michael.

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