Obituary Prof. John Nelder

This article was originally published in The Times on Friday 27th August 2010.

Influential statistician who made lasting and far-reaching contributions to theory and pratice in his field

John Nelder greatly influenced academic statistics, but the bulk of his career was spent in agricultural research institutions.

When he began his work scientific research produced copious numerical data but this had to be analysed manually. Calculating machinery at the time was largely a range of desk-mounted calculators that could handle such tasks as long division and long multiplication by turning a handle on the older versions or by pressing buttons on the newer electrical machines.

The computer age began in the 1940s, in response to wartime demands; by the 1950s mainframe computers were becoming available for universities and research institutions, but these were large, slow and expensive. Programming used general-purpose computing languages, and had to be done by punched cards, a procedure that was slow and notoriously prone to error.

He helped to expose a fraud involving rare birds and a taxidermist

Standard statistical work is variable in detail, but the users can usually tailor the programme to their own needs by suitable additions or modifications. The idea was to combine the flexibility of a programming language with the simplicity of operation of a package. Nelder was one of the pioneers of Gen­stat ("general statistical package") from 1966, and GLIM ("generalised linear models") from 1974. Both have gone through many versions, are still widely used, and have been very successful.

John Ashworth Nelder was born in 1924 in Dulverton, Somerset, and educated at Blundell's School at Tiverton, Devon and Sidney Sussex College, Cambridge, where he read mathemat­ics. He became head of the statistics section at the National Vegetable Research Station at Wellesbourne in Warwickshire in 1951.

In 1968 he left Wellesbourne to be head of the statistics department at Rothamsted Experimental Station in Harpenden, Hertfordshire, where he remained until 1984. He developed close links with academic statistics, and was a visiting professor in the mathe­matics department of Imperial College, London from 1972 to 2009.

His most important contributions to statistical theory concerned generalisations of regression. This is the part of statistics where one has a variable of interest, to be predicted say, and uses the information in other variables (called covariates) that one can measure to make such a prediction. The standard procedure is to use a linear combination (sum of multiples) of the covariates as the "systematic part", and add a random error. The error is usually taken to be normally distributed – at best an approximation, as all values would then be possible, while such variables as height and weight are necessarily positive. Nelder's work with Robert Wedderburn in 1972 on generalised linear models provided the theoretical framework to handle such situations. His book on the subject with Peter McCullagh (in its 1983 and 1989 editions) integrates the theory with computer implementation in GLIM or Genstat. It is widely applied in such areas as survival analysis in medical statistics, and analysis of data involving counts rather than measurements, common in the social sciences.

Nelder was one of the pioneers of the approach to statistics based on likelihood (a concept introduced by the great statistician Sir Ronald Fisher in 1912). With Mead, he introduced the Nelder-Mead simplex method for response-surface optimisation, widely used in engineering and statistics.

He also worked on design of experiments, an area of statistics pioneered by his predecessor Fisher at Rothamsted in the 1920s. Nelder's last book, with Younjo Lee and Yudi Pawitan, on generalised linear models with random effects and their analysis via "hierarchical" likelihood methods, was published in 2006, when he was already 81, but still very active.

In 1962, after a statistical examination, he helped to expose the Hastings Rarities affair, a fraud involving rare birds preserved by a taxidermist.

Like many mathematicians, Nelder was very musical. He was a fine pianist, and would entertain guests at his home in Redbourne, Hertfordshire, by playing Mozart sonatas or singing comic songs, accompanying himself at the piano.

Nelder was elected a Fellow of the Royal Socliety in 1981. He was president of the Royal Statistical Society in 1985-86; he received its Guy Medal in silver in 1977 and the Guy Medal in gold in 2005. His 80th birthday was celebrated by the publication of a festschrift in his honour edited by colleagues at Imperial College.

He is survived by his wife, Mary, whom he married in 1955, and their son and daughter.

Professor J. A. Nelder, FRS, statistician, was born on October 8, 1924. He died on August 7, 2010, aged 85.