Peter Whittle, who died on 10 August 2021 at 94 years of age, will be remembered as a pioneer across the fields of probability, statistics and optimization. He wrote a number of important papers, but it is in his books that one can best appreciate the broad sweep of his achievements and the simplicity, unity and generality of his approach. His twelve major volumes covered times series, prediction, constrained optimization, dynamic programming, optimal control, stochastic systems, the foundations of probability theory and neural nets. Several of these works were ahead of their time: indeed some of his early works appear to have been written for the audience of today, such is the extent to which they anticipated subsequent developments.
Peter Whittle was born in Wellington, New Zealand, in February 1927, graduating from the University of New Zealand with a BSc in mathematics and physics in 1947 and an MSc in mathematics in 1948. He intended a career in mathematical physics, but vacation work in the NZ Department of Scientific and Industrial Research (DSIR) offered statistical problems from agriculture and biometrics that attracted his scientific interest, and his first paper was on the design of experiments.
A travelling scholarship in 1949 took Peter to Uppsala, Sweden, for his doctoral work under Hermann Wold. A profound influence on Peter was Maurice Bartlett, then working in Manchester. Peter began his work on time series analysis, and in his doctoral thesis and four subsequent papers, he essentially solved the large-sample inference problem for a stationary time series generated by a linear Gaussian model. The terms “multivariate Whittle likelihood” and “Whittle estimation” are now common, but this early groundbreaking work was not at the time widely appreciated: Peter remarked that, perhaps in unconscious emulation of the admired Bartlett, he wrote too gnomically. In marked contrast his corresponding analysis for spatial processes, published in 1954, had an immediate and sustained impact. His asymptotic inference theory for Gaussian processes and related spatial processes was ahead of its time in considering power law covariance functions, which are now central in image analysis.
In 1952 as an unknown young PhD, Peter made his first visit to the Statistical Laboratory, Cambridge. He fondly described the experience: John Wishart politely pretended to know who he was and gave him a cup of tea; Frank Anscombe’s courtesy was plainly innate; and Henry Daniels regarded him with quizzical amiability.
After Uppsala, Peter returned in 1953 to New Zealand and the DSIR: his work on NZ rabbits (pests of the first order) produced the Whittle threshold theorem for stochastic process models of an epidemic. Oscillations in oceanographic data uncovered non-linear effects. His time-series work led into the study and statistical analysis of spatial models. During this period Peter also became interested in polymerisation and in reversibility, both topics he would return to later. Peter believed that his subsequent interests and career were largely shaped by his time here, working on problems from geophysics, agriculture and industry. His superior there later wrote “His genuine interest in people and their work, his boyish sense of humour and lack of pretension, made it possible for him to carry his own intellectual pre-eminence without exciting jealousy or antagonism.”
Peter returned to Britain in 1959 as a lecturer in the Statistical Laboratory, Cambridge, where his colleagues were Dennis Lindley and Maurice Walker, and where his research students included John Bather and John Kingman. In 1961 he moved to the Chair of Mathematical Statistics at Manchester, succeeding Maurice Bartlett and with David Silvey and Toby Lewis as colleagues, and with Henry Daniels in Birmingham as a kindred spirit. Peter’s interest in optimization developed at Manchester; he kept his interest in spatial processes, with his student David Brook producing an early result on Markov random fields; and he obtained his first results on networks of queues and partial balance.
In 1967 Peter returned to Cambridge as the Churchill Professor of Mathematics for Operational Research, a newly established chair endowed by Esso through the active management of David Kendall. The position gave Peter the perfect platform for his vision that what needed developing was not just narrow sense operational research, but the whole area of what in Cambridge is now termed applicable mathematics. This includes, for example, probability, statistics, optimization, game theory and those aspects of disciplines such as control theory, communications theory and mathematical economics which might be pursued by someone technically based in probability and optimization. Developments in the US had convinced Peter of not only the practical importance of these topics but also the depth and coherence of the theory they generate. He felt that the subject of statistics itself is thoroughly penetrated by optimization concepts and is only viewed aright when embedded in this larger context (a view now taken for granted in statistics generally and in areas such as machine learning). Peter set about the task of creating the new courses to deliver this vision, and this began an evolution of the Mathematical Tripos at Cambridge that has continued to this day. He served as Director of the Cambridge Statistical Laboratory from 1973-1986.
By the time of Peter’s second major work on time series (Prediction and Regulation, 1963, revised 2nd ed. 1983) his interest had moved from inference to prediction and control. His four volumes on optimization marked his continuing interest in stochastic control, and in temporal optimization generally, using dynamic programming ideas. Optimization under Constraints (1971) is shot through with insight in a prose style combining power and economy. Notable in Optimization over Time (1983) is Peter’s treatment of the multi-armed bandit problem. Despite its whimsical name this problem – the sequential allocation of effort in the presence of uncertainty –arises in areas as varied as the design of clinical trials or the choice of exploration avenues in artificial intelligence. The problem was first formulated during World War II and, as Peter famously remarked, efforts to solve it so sapped the energies of Allied analysts that the suggestion was made that the problem be dropped over Germany, as the ultimate instrument of intellectual sabotage. Later, in Risk-Sensitive Optimal Control (1991) the very complete theory for the linear/quadratic/Gaussian case is transferred to a significantly more general case.
His vision for the whole area of applicable mathematics was by now well established, providing the mathematical foundations for central areas of engineering and economics. Mathematicians often do not see the impact of their work on other fields. It is noteworthy that in the Foreword to the second edition of Prediction and Regulation, Thomas Sargent, later awarded the Nobel Prize in Economics for empirical research on cause and effect in the macroeconomy, writes on the importance of Peter’s work for understanding dynamic economic phenomena.
His book Probability via Expectation (1970, expanded in 2000) is an exposition of probability theory that formulates its axioms in terms of expectation rather than measure – in Peter’s view, this approach has advantages at many levels. One advantage is that probability theory and probability of quantum theory are seen to differ in only a modification of the axioms – a modification rich in consequences, but (as in so much of Peter’s work) succinctly expressible. The book was published in Russian in 1982, quite a compliment in view of the special role Russian authors played in the development of probability theory.
Peter had a life-long interest in statistical/physical models, and the book Systems in Stochastic Equilibrium (1986) collects as one of its parts Whittle’s work on polymerization and random graphs, and also his work on partial balance in networks. His work on networks continued with Neural Nets and Chaotic Carriers (1998) and Networks: Optimization and Evolution (2007). In his final years he maintained his interest in neural nets, finding the notions of self-optimizing and self-organizing systems both fascinating and of enormous potential. But even he might have been surprised to see the pace of the ongoing realignment of mathematics, with statistics, optimization and machine learning permeating applied mathematics and leading to remarkable advances across swathes of physical, biological and social science.
Peter considered himself fortunate in the colleagues he found in English academic life, whose qualities he thought included goodwill and a presumption of goodwill, leading to a cheerful directness and unspoken community. Among numerous honours, he was awarded the RSS Guy Medals in both Silver (1966) Gold (1996); the Sylvester Medal of the Royal Society, and the INFORMS Lanchester Prize and John von Neumann Theory Prize. He was a Fellow of the Royal Society and of IMS, and an International Member of the US National Academy of Engineering.
Peter Whittle married Käthe Blomquist in 1951, and they had six children. Käthe was Finnish and they had met in Uppsala. They did their courting in Swedish, their only common language.
At school in New Zealand Whittle played the flute, and he got pleasure from making and playing instruments throughout his life. Languages were another interest: French, Swedish and Russian early in his life, and after retirement Scottish Gaelic whose evocative charms fascinated him. He was a talented runner (achieving 4 minutes 36 seconds for the mile) and kept up distance running into his later years. He enjoyed carpentry, DIY and toymaking, finding them a useful counterweight to his academic work.
Peter’s wife Käthe died in 2020. He is survived by their six children, seven grandchildren and one great granddaughter. Throughout his life he greatly missed New Zealand, and asked that his ashes be cast into the waters of Island Bay, Wellington, New Zealand, which he had grown up overlooking.
This is an abridged version of an obituary by Frank Kelly, Statistical Laboratory, University of Cambridge, and published by the Royal Statistical Society.