John Ashworth Nelder (8 October 1924 – 7 August 2010) was a British statistician known for his contributions to

experimental design The design of experiments (DOE), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. ...

analysis of variance Analysis of variance (ANOVA) is a family of statistical methods used to compare the Mean, means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation ''between'' the group means to the amount of variati ...

computational statistics Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational ...

, and

statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...

Contributions

Nelder's work was influential in statistics. While leading research at

Rothamsted Experimental Station Rothamsted Research, previously known as the Rothamsted Experimental Station and then the Institute of Arable Crops Research, is one of the oldest agricultural research institutions in the world, having been founded in 1843. It is located at Harp ...

, Nelder developed and supervised the updating of the

statistical software The following is a list of statistical software. Open-source * ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management * ADMB – a software suite for non-linear statistical modeling based on C+ ...

packages

GLIM GLIM or Glim may refer to: * Glim, a neighborhood in Alexandria, Egypt * GLIM (software) (Generalized Linear Interactive Modelling), a statistical software program for fitting generalized linear models * Jonas Glim, a DC Comics character * Glim (o ...

and GenStat: Both packages are flexible

high-level programming language A high-level programming language is a programming language with strong Abstraction (computer science), abstraction from the details of the computer. In contrast to low-level programming languages, it may use natural language ''elements'', be ea ...

s that allow statisticians to formulate linear models concisely. GLIM influenced later environments for

statistical computing Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational ...

such as

S-PLUS S-PLUS is a commercial implementation of the S (programming language), S programming language sold by TIBCO Software Inc. It features object-oriented programming capabilities and advanced analytical algorithms. Its statistical analysis capabilit ...

and R. Both GLIM and GenStat have powerful facilities for the

for

block Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 ...

experiments An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome o ...

, an area where Nelder made many contributions. In

, Nelder proposed the

generalized linear model In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by ...

together with Robert Wedderburn. Nelder and Wedderburn formulated generalized linear models as a way of unifying various other statistical models, including

linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...

logistic regression In statistics, a logistic model (or logit model) is a statistical model that models the logit, log-odds of an event as a linear function (calculus), linear combination of one or more independent variables. In regression analysis, logistic regres ...

and

Poisson regression In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable ''Y'' has a Poisson distribution, and assumes the lo ...

. They proposed an

iteratively reweighted least squares The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form of a ''p''-norm: \mathop_ \sum_^n \big, y_i - f_i (\boldsymbol\beta) \big, ^p, by an iterative meth ...

method Method (, methodos, from μετά/meta "in pursuit or quest of" + ὁδός/hodos "a method, system; a way or manner" of doing, saying, etc.), literally means a pursuit of knowledge, investigation, mode of prosecuting such inquiry, or system. In re ...

for

maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stati ...

estimation of the model parameters. In

statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of ...

, Nelder (along with George Barnard and

A. W. F. Edwards Anthony William Fairbank Edwards, Fellow of the Royal Society, FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 1935) is a British statistician, geneticist and evolutionary biologist. Ed ...

) emphasized the importance of the

likelihood A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the j ...

data analysis Data analysis is the process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data modeling, modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Da ...

, promoting this "likelihood approach" as an alternative to

frequentist Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or pro ...

and

Bayesian Thomas Bayes ( ; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian ( or ) may be either any of a range of concepts and approaches that relate to statistical methods based on Bayes' theorem Bayes ...

statistics. In response-surface

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...

, Nelder and Roger Mead proposed the Nelder–Mead method ">Nelder–Mead simplex heuristic, widely used in engineering and statistics.

Biography

Born in Brushford, near Dulverton">Brushford, Somerset">Brushford, near Dulverton, Somerset, Nelder was educated at Blundell's School">Dulverton.html" ;"title="Brushford, Somerset">Brushford, near Dulverton">Brushford, Somerset">Brushford, near Dulverton, Somerset, Nelder was educated at Blundell's School and Sidney Sussex College, Cambridge, where he read Mathematics. Nelder's appointments included Head of the Statistics Section at the Horticulture Research International, National Vegetable Research Station, Wellesbourne, from 1951 to 1968 and head of the Statistics Department at

from 1968 to 1984. During his time at Wellesbourne he spent a year (1965–1966) at the Waite Institute in Adelaide, South Australia, where he worked with Graham Wilkinson on Genstat. He held an appointment as visiting professor at

Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...

from 1972 onwards. He was responsible, with

Max Nicholson Edward Max Nicholson (12 July 1904 – 26 April 2003) was a pioneering environmentalist, ornithologist and internationalist, and a founder of the World Wildlife Fund. Early life Max Nicholson, as he was known to all, was born in Kilternan, ...

and

James Ferguson-Lees Ian James Ferguson-Lees (8 January 1929 in Italy – 11 January 2017) was a British ornithologist. He became known as a member of the British Birds Rarities Committee who was responsible, with John Nelder and Max Nicholson, for publicly debunkin ...

, for debunking the

Hastings Rarities The Hastings Rarities affair is a case of statistically demonstrated ornithology, ornithological fraud that misled the bird world for decades in the 20th century. The discovery of the long-running hoax shocked ornithologists. The Hastings Rarit ...

– sightings of a series of rare birds, preserved by a

taxidermist Taxidermy is the art of preserving an animal's body by mounting (over an armature) or stuffing, for the purpose of display or study. Animals are often, but not always, portrayed in a lifelike state. The word ''taxidermy'' describes the process ...

and provided with bogus histories.Nelder, J.A. (1962). A statistical examination of the Hastings Rarities. '' British Birds'', August 1962. Nelder died on 7 August 2010 in Luton and Dunstable Hospital, taken there after a fall at home, which was incidental to the cause of death.

Awards and distinctions

Nelder was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 1976 and received the

Royal Statistical Society The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good. ...

Guy Medal The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Silver and Bronze medals are awarded annually. The Gold Medal was awarded every three years between 1987 and 2011, but is awarded bienni ...

in Gold in 2005. He was also the recipient of the inaugural Karl Pearson Prize of the

International Statistical Institute The International Statistical Institute (ISI) is a professional association of statisticians. At a meeting of the Jubilee Meeting of the Royal Statistical Society, statisticians met and formed the agreed statues of the International Statistical ...

, with

Peter McCullagh Peter McCullagh (born 8 January 1952) is a Northern Irish-born American statistician and John D. MacArthur Distinguished Service Professor in the Department of Statistics at the University of Chicago. Education McCullagh is from Plumbridge, ...

, "for their monograph Generalized Linear Models (1983)". As tribute on his eightieth birthday, a

festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the h ...

''Methods and Models in Statistics: In Honour of Professor John Nelder, FRS'' was edited by Niall Adams, Martin Crowder, David J Hand & Dave Stephens, Imperial College Press (2004). The first annual John Nelder memorial lecture was held at Imperial College London, on 8 March 2012, as part of the Mathematics department Colloquium series. The lecture was given by Nelder's long term co-author,

. An interviewPodcast
ma.ic.ac.uk with McCullagh, about statistical modelling, includes some reminiscences about Nelder.

Selected publications

* JN and R. W. M. Wedderburn, "Generalized Linear Models", ''J. R. Statist. Soc.'' A, 135 (1972) 370–384. * McCullagh, P. and J.A. Nelder. 1989. ''Generalized Linear Models''. 2nd ed. Chapman & Hall/CRC, Boca Raton, Florida. *Lee, Y., J.A. Nelder, and Y. Pawitan. 2006. ''Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood''. Chapman & Hall/CRC, Boca Raton, Florida.

References

External links

A Conversation with John Nelder

{{DEFAULTSORT:Nelder, John Fellows of the Royal Society Presidents of the Royal Statistical Society Rothamsted statisticians English statisticians Academics of Imperial College London 20th-century British mathematicians 21st-century British mathematicians Alumni of Sidney Sussex College, Cambridge People educated at Blundell's School People from Dulverton 1924 births 2010 deaths Rothamsted Experimental Station people Computational statisticians