Photo courtesy of Rowan Lindley

Dennis Lindley, a key figure in the modern Bayesian school of statistics, died on 14 December 2013 at the age of 90. The pervasive and growing influence of Bayesian methodology on data analysis and decision making might not have happened without the advocacy and persistence of Lindley and a small number of colleagues.

Lindley was born on 25 July 1923 in London, as the only child of a builder. His first ambition was to become an architect, but that became impracticable with the start of World War 2, and instead he was encouraged by his mathematics teacher to try for Cambridge University. He passed the entrance examinations and went to Cambridge in 1941. After being awarded a first class degree in mathematics, Lindley expected to go into the armed forces, but instead was offered a position in the Ministry of Supply, on condition that he attended a statistics course taught by Oscar Irwin.

Lindley later claimed not to have understood Irwin’s course, but he nevertheless joined the Civil Service. As well as practical work on statistical quality control and analysis of military test data, Lindley and his colleagues were encouraged to read the key papers in statistics.

After the war, Lindley worked at the National Physical Laboratory, where he published his first paper, a short contribution in Nature in August 1946, on problems in regression. This brief work already shows some of the characteristics of many of Lindley’s later publications: a precise definition of the problem, an appropriately mathematical approach, and polite but firm pointing out of errors made by others.

Lindley returned to Cambridge for a further year of study, taking all the statistics courses he could. Then, in 1948, he accepted an academic post at Cambridge, eventually becoming Director of the Statistical Laboratory.

In his early years at Cambridge, Lindley said that his aim was to provide an axiomatic basis for the frequentist statistical approaches of Fisher, Neyman and Pearson, thus giving them a respectable mathematical basis. Indeed, he read a paper with this aim to the Royal Statistical Society in 1953, taking an approach which (according to Egon Pearson) contained “some very stiff mathematics.” Lindley was not the only one attempting this general approach; the first edition of Jimmie Savage’s Foundations of Statistics, published in 1954, had the same aim. Lindley visited Savage in Chicago in 1954. This interaction, and work with Jack Good, Robert Schlaifer, Bruno de Finetti and others, led to the emergence of a distinctive Bayesian perspective, and in the case of Lindley to a clear subjective Bayesianism. But it also led to serious tensions with the frequentist school, particularly salient at the Fourth Berkeley Symposium in 1960.

Lindley was appointed to the new Chair of Statistics at the University College of Wales, Aberystwyth in 1960. When he moved to University College London in 1967, the contrast between Lindley’s approach and the previous orientation of the department was stark. Pat Rivett commented, “It was as though a Jehovah’s Witness had been elected Pope.” At UCL Lindley was in charge of a vibrant, and largely Bayesian, department—among others, Philip Dawid and Mervyn Stone were teaching there, and Adrian Smith, Jose Bernardo and Tony O’Hagan were among the doctoral students.

But Lindley (later) claimed to dislike administration, and to be bad at it. He discovered that new UCL regulations allowed him to retire early, and in 1977 at the age of 54 he did just that. But he did not retire from statistics. He divided his time between his home in the west of England and travelling to collaborate with colleagues around the world. He was a founder of the regular Valencia International Meetings on Bayesian statistics, in which he participated enthusiastically for many years.

Dennis Lindley predicted that the 21st century would be Bayesian. In some ways this prediction has come to fruition, driven partly by the development of powerful computing approaches. In a broad sense, we are all sometimes Bayesian. But, while Lindley generally approved of the move to computational and applied work, he remained convinced of the need for a strong philosophical underpinning. In a 1990 paper on the philosophy of statistics, he wrote disapprovingly of one of the Valencia meetings that “many participants did not seem to me fully to appreciate the Bayesian philosophy.”

Lindley was the recipient of several honours, including the Royal Statistical Society’s Guy Medal in Gold (2002), as well as the informal but enduring honour of having statistical concepts named after him (including Lindley’s paradox in inference and Lindley’s equation in stochastic processes). He will be missed and mourned.

Lindley is survived by his wife Joan and their three children.

Written by Professor Kevin McConway, The Open University, UK