Contributions
Nelder's work was very influential in statistics. While leading research at Rothamsted Experimental Station, Nelder developed and supervised the updating of the statistical software packages GLIM and GenStat: Both packages are flexible high-level programming languages that allow statisticians to formulate linear models concisely. GLIM influenced later environments for statistical computing such as S-PLUS and R. Both GLIM and GenStat have powerful facilities for the analysis of variance for block experiments, an area where Nelder has made many contributions.
In statistical theory, Nelder and Wedderburn proposed the generalized linear model. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters.
In statistical inference, Nelder (along with George Barnard and A. W. F. Edwards) has emphasized the importance of the likelihood in data analysis, promoting this "likelihood approach" as an alternative to frequentist and Bayesian statistics.
In response-surface optimization, Nelder and Roger Mead proposed the Nelder-Mead simplex heuristic, which is often used in engineering and statistics.
Read more about this topic: John Nelder