Mathematician who was a leading figure in the Bayesian school of statistics
Dennis Lindley, who has died aged 90, was one of the modern founders of the "Bayesian" school of statistics, an approach to inference that has had a dramatic effect on how we analyse data. Our increasing reliance on quantitative evidence when making decisions means that this work has had a vast impact – in medicine, commerce, science, and indeed in just about all walks of life.
Lindley said his aim in his early years as an academic was to make statistics a respectable branch of mathematics: all the other courses he had studied had the classic mathematical form, of a system of axioms from which the consequences were deduced, but statistics lacked this. As a consequence, Lindley initially saw his work as providing a solid mathematical base for the then dominant frequentist school of statistics, and only later recognised that in fact he had produced something rather different.
When he visited the US mathematician Jimmie Savage in Chicago, he discovered that Savage had arrived at a similar perspective on probability to his, and indeed so had others, including Bruno de Finetti in Italy, Jack Good and Harold Jeffreys in the UK, and Robert Schlaifer in the US. It was this perspective that led to the Bayesian school of statistics.
The contrast between the frequentist and Bayesian perspectives is deep. The frequentist approach evaluates the accuracy of an estimate of an unknown value in terms of how different that estimate could have been. The Bayesian approach updates personal beliefs about the unknown true value. The former is an objective statement about the values of statistics generated from a given model; the latter is a subjective statement about beliefs. It was this latter perspective that led to De Finetti's famous remark, "probability does not exist".
By the time of the Fourth Berkeley Symposium on Statistics in California (1960), tensions between the two schools were emerging, and some outspoken exchanges took place. When Lindley moved to University College London, the radically different statistical philosophy he brought with him led Pat Rivett to remark that "it was as though a Jehovah's Witness had been elected pope".
Lindley, an only child, was born in Surbiton, south-west London. His father was a roofer, and, inspired by the plans his father brought home, Lindley's early ambition was to be an architect. He attended Tiffin school in Kingston upon Thames, where one of his teachers spotted his mathematical ability and suggested he try forCambridge. He won a minor scholarship to Trinity College, and went there in 1941. He attributed his success in this to the one-on-one instruction he got from his teacher while sitting in the school's bomb shelter after air-raid warnings.
Degree courses at the time lasted only two years, and after being awarded a first-class degree he was expecting to have to join the armed forces. However, he was approached about a position in the Ministry of Supply, provided he attended a statistics course, taught by Oscar Irwin.
Lindley described his time in the civil service, working under George Barnard, as like being one of a group of PhD students, although without a supervisor. In addition to practical work, they studied important statistical papers, and Lindley took the opportunity to spend his weekends at Birkbeck College, London, studying with the mathematician Paul Dienes.
After the war, Lindley joined the National Physical Laboratory in Teddington, west London, and then went back to Cambridge for a third year, taking all the statistics courses he could, including one by Jeffreys, another of the key players in the Bayesian revolution.
In 1948, Lindley accepted an offer of a post at Cambridge, initially as a demonstrator, working his way up to become director of the statistical laboratory. In 1960, he was appointed to the new chair of statistics at the University College of Wales at Aberystwyth, and seven years later took up the chair of statistics at University College London.
He found that new UCL regulations would enable him to retire at the early age of 54, although, as with many academics, this did not mean that he stopped working. Subsequently he spent his summers in Minehead in Somerset and his winters travelling to collaborate with academic colleagues around the world. Although enjoying the peace and quiet of retirement, he said that one of his regrets was that he did not have the stimulus of young PhD students to work with.
In 1975, Lindley entitled a paper The Future of Statistics – a Bayesian 21st Century, and Bayesian methods have indeed become pervasive, enabled by the development of powerful computing facilities. Nowadays, the word Bayesian carries tremendous cachet. This can even be to the extent that sometimes the mere use of Bayes' theorem, a purely mathematical result with which all statisticians, of whatever stripe, agree, is referred to as a Bayesian analysis, without necessarily accepting the notion of a distribution for the underlying unknown process characteristics which lies at the heart of Bayesian statistics.
Lindley received various honours, including the Royal Statistical Society's Guy Medal in Gold (2002), and has various statistical objects named after him, including Lindley's paradox and Lindley's equation. He also coined the expression "Cromwell's rule", which essentially says that one should never assert something to be either completely impossible or completely certain, unless it is logically so. His phrase was based on Oliver Cromwell's letter to the synod of the Church of Scotland, in which he said "I beseech you, in the bowels of Christ, think it possible that you may be mistaken."
Lindley is survived by his wife, Joan, whom he married in 1947, and their three children, Janet, Rowan and Robert.
• Dennis Victor Lindley, mathematician, born 25 July 1923; died 14 December 2013