Ronald Fisher advocated testing using p-values, Harold Jeffreys proposed use of objective posterior probabilities of hypotheses and Jerzy Neyman recommended testing with fixed error probabilities. Each was quite critical of the other approaches. Most troubling for statistics and science is that the three approaches can lead to quite different practical conclusions.

This article focuses on discussion of the conditional frequentist approach to testing, which is argued to provide the basis for a methodological unification of the approaches of Fisher, Jeffreys and Neyman. The idea is to follow Fisher in using p-values to define the "strength of evidence" in data and to follow his approach of conditioning on strength of evidence; then follow Neyman by computing Type I and Type II error probabilities, but do so conditional on the strength of evidence in the data. The resulting conditional frequentist error probabilities equal the objective posterior probabilities of the hypotheses advocated by Jeffreys.

On February 12, 2001 the Human Genome Project announced the completion of a draft physical map of the human genome---the genetic blueprint for a human being. Now the challenge is to annotate this map by understanding the functions of genes and their interplay with proteins and the environment to create complex, dynamic living systems. This is the goal of functional genomics. Recent technological advances enable biomedical investigators to observe the genome of entire organisms in action by simultaneously measuring the level of activation of thousands of genes under the same experimental conditions. This technology, known as microarrays, today provides unparalleled discovery opportunities and is reshaping biomedical sciences. One of the main aspects of this revolution is the introduction of computationally intensive data analysis methods in biomedical research. This article reviews the foundations of this technology and describes the statistical challenges posed by the analysis of microarray data.

DNA microarrays are part of a new and promising class of biotechnologies that allow the monitoring of expression levels in cells for thousands of genes simultaneously. An important and common question in DNA microarray experiments is the identification of differentially expressed genes, that is, genes whose expression levels are associated with a response or covariate of interest. The biological question of differential expression can be restated as a problem in multiple hypothesis testing: the simultaneous test for each gene of the null hypothesis of no association between the expression levels and the responses or covariates. As a typical microarray experiment measures expression levels for thousands of genes simultaneously, large multiplicity problems are generated. This article discusses different approaches to multiple hypothesis testing in the context of DNA microarray experiments and compares the procedures on microarray and simulated data sets.

We propose a new method for class prediction in DNA microarray studies based on an enhancement of the nearest prototype classifier. Our technique uses "shrunken" centroids as prototypes for each class to identify the subsets of the genes that best characterize each class. The method is general and can be applied to the other high-dimensional classification problems. The method is illustrated on data from two gene expression studies: lymphoma and cancer cell lines.

John Ashworth Nelder was born in 1924 in Dulverton, Somerset, England. He received his secondary education in nearby Tiverton at Blundell's, a "public" [that is to say, privately funded] school that he attended as a day pupil. In 1942, he entered Sidney Sussex College, Cambridge University, to read mathematics. His studies were interrupted after one year by war service and he trained as an RAF navigator in South Africa. He returned to Cambridge in 1946 and complete his studies, graduating a "wrangler" [the Cambridge University term for one who graduates with a first in mathematics] in 1948. He stayed on at Cambridge for a further year and completed the diploma in statistics in 1949.

In 1950, he was appointed head of the statistics section at the National Vegetable Research Station at Wellesbourne. In 1955, he married Mary Hawkes. They have a son and a daughter. He spent one year (1965-1966) on leave of absence from Wellesbourne in Adelaide as a research fellow at the Waite Institute. During this time, he started to develop the computer program, Genstat, which incorporated ideas of "general balance" that he had developed for the design and analysis of experiments. In 1968, John succeeded Frank Yates as head of statistics at Rothamsted Experimental Station, Harpenden. At Rothamsted, developing ideas he had earlier published in Biometrics, he started a collaboration with Wedderburn that resulted in a paper on generalized linear models that was to revolutionize statistical analysis. This modeling approach formed the sole raison d'être of the statistical package GLIM and is now incorporated in other major statistical packages such as Genstat, Splus and SAS. During his time at Rothamsted, he was appointed as a visiting professor at Imperial College London (1972), which led to his collaboration with Peter McCullagh in writing a book, Generalized Linear Models. Since his retirement in 1984, he has continued as a visiting professor in the Department of Mathematics at Imperial. He is a familiar figure at Harpenden Station, waiting to catch the train to London.

John Nelder has received many honors for his statistical work. He was awarded the Guy Medal in Silver of the Royal Statistical Society in 1977 and elected a Fellow of the Royal Society in 1981. He has served both the International Biometrics Society (1978-1979) and the Royal Statistical Society (1985-1986) as president. In 1981, the Université Paul Sabatier, Toulouse, granted him and honorary D.Sc. He has published two books and over a hundred papers, but these numbers do not do justice to his influence on statistical modeling, which is enormous. A hallmark of his work is the way that statistical and mathematical insight is combined with deep numerical, algorithmic and computational understanding to forge original analytic tools of great generality and high applicability. He is unusual among theoreticians in the practical interest he has shown in planning experiments and analyzing data. Since his retirement, he has continued to be active in research and has started a collaboration on hierarchical generalized linear models with Youngjo Lee. In this work, he hopes to do for random-effect models of the exponential class what he has already achieved for fixed-effect models.