Sir Ronald Aylmer Fisher
Born: 17 Feb 1890 in London, England
Died: 29 July 1962 in Adelaide, Australia
R A Fisher's parents were Katie Heath and George Fisher. In 1904 Ronald entered Harrow. He
excelled at Harrow winning the Need Medal in 1906 in a mathematical essay competition open to
the whole school. Fisher was awarded a £80 scholarship from Ciaos and Bonville College, Cambridge,
which was necessary to finance his studies since his father had lost his fortune. In October 1909 he
matriculated at Cambridge. Although he studied mathematics and astronomy at Cambridge, he was
also interested in biology. He graduated with distinction in the mathematical tripos of 1912.
Awarded a Wollaston studentship, he continued his studies at Cambridge under Stratton on the
theory of errors reading Airy’s manual the Theory of Errors. It was Fisher's interest in the theory of
errors that eventually led him to investigate statistical problems.
After leaving Cambridge, he returned to London, taking up a post as a statistician in the
Mercantile and General Investment Company. When war broke out in 1914 he
enthusiastically tried to enlist in the army, having already trained in the Officers' Training
Corps while at Cambridge. His medical test showed him A1 on all aspects except his
eyesight, which was rated C5, so he was rejected. He became a teacher of mathematics and
physics, teaching at Rugby and other similar schools between 1915 and 1919.
The interest in eugenics, and his experiences working on the Canadian farm, made Fisher
interested in starting a farm of his own. Fisher married Ruth Eileen at a secret wedding
ceremony without her mother's knowledge, on 26 April 1917, only days after Ruth Eileen's
17th birthday. They had two sons and seven daughters, one of whom died in infancy.
Fisher gave up being a mathematics teacher in 1919 when he was offered two posts
simultaneously. Karl Pearson offered him the post of chief statistician at the Galton
laboratories and he was also offered the post of statistician at the Rothamsted Agricultural
Experiment Station. This was the oldest agricultural research institute in the United Kingdom,
established in 1837 to study the effects of nutrition and soil types on plant fertility, and it
appealed to Fisher's interest in farming. He accepted the post at Rothamsted where he made
many contributions both to statistics, in particular the design and analysis of experiments, and
to genetics.
There he studied the design of experiments by introducing the concept of randomisation and
the analysis of variance, procedures now used throughout the world. Fisher's idea was to
arrange an experiment as a set of partitioned sub-experiments that differ from each other in
having one or several factors or treatments applied to them. The sub-experiments were
designed in such a way as to permit differences in their outcome to be attributed to the
different factors or combinations of factors by means of statistical analysis. This was a
notable advance over the existing approach of varying only one factor at a time in an
experiment, which was a relatively inefficient procedure.
In 1921 he introduced the concept of likelihood. The likelihood of a parameter is proportional
to the probability of the data and it gives a function which usually has a single maximum
value, which he called the maximum likelihood. In 1922 he gave a new definition of
statistics. Its purpose was, he claimed, the reduction of data, and he identified three
fundamental problems. These are:
i.
ii.
iii.
specification of the kind of population that the data came from;
estimation; and
distribution.
Fisher published a number of important texts; in particular Statistical Methods for Research
Workers (1925) ran to many editions which he extended throughout his life. It was a
handbook for the methods for the design and analysis of experiments which he had developed
at Rothamsted. The contributions Fisher made included the development of methods suitable
for small samples, like those of Gosset, and the discovery of the precise distributions of many
sample statistics. Fisher published the design of experiments (1935) and Statistical tables
(1947).
While at the Agricultural Experiment Station he had conducted breeding experiments with
mice, snails and poultry, and the results he obtained led to theories about gene dominance and
fitness which he published in The Genetical Theory of Natural Selection (1930).
This work on natural selection led Fisher to question the way that in civilised society’s weak
and relatively infertile people obtained advantages over strong healthy individuals. He felt
that the natural survival of the fittest method of improving the human race was being
artificially changed by factors that specifically benefited the less well adapted. A strong
advocate of measures to counter this trend, he proposed that family allowances should be
proportional to income to support the well-adapted healthy members of society. As one might
expect, this policy was very unpopular and he found few supporters.
In 1933 Karl Pearson retired as Galton Professor of eugenics at University College and Fisher
was appointed to the chair as his successor. Fisher held this post for ten years, being
appointed as Arthur Balfour professor of genetics at the University of Cambridge in 1943.
Before this, however, he had moved away from London when war broke out in 1939, finding
temporary accommodation at Sharpened. He retired from his Cambridge chair in 1957 but
continued to carry out his duties there for another two years until his successor could be
appointed. He then moved to the University of Adelaide where he continued his research for
the final three years of his life.
In 1918 Fisher submitted his very important paper on the correlation between relatives on the
supposition of MendeliIan inheritance to the Royal Society. Two referees, R C Punnet and
Pearson, were appointed and reported on the paper. Neither referee rejected the paper;
however, they both merely expressed reservations and stated clearly that there were aspects
of the paper that they were not competent to judge. In the event Fisher withdrew the paper
and submitted it to the Transactions of the Royal Society of Edinburgh where it was accepted.
It is not surprising that Fisher's novel ideas took time to become accepted.
Fisher was elected a Fellow of the Royal Society in 1929, was awarded the Royal Medal of the
Society in 1938, and was awarded the Darwin Medal of the Society in 1948:He was elected to the American Academy of Arts and Sciences in 1934, the American Philosophical
Society in 1941, the International Society of Haematology in 1948, the National Academy of Sciences
of the United States in 1948, and the Deutsche Akademie der Naturforscher Leopoldina in 1960.
Various institutions awarded him an honorary degree including Harvard University (1936), University
of Calcutta (1938), University of London (1946), University of Glasgow (1947), University of Adelaide
(1959), University of Leeds (1961), and the Indian Statistical Institute (1962). He was knighted in
1952.
Fisher's character is describedas follows:- He was capable of tremendous charm, and warmth
in friendship. But he also was the victim, as he himself recognised, of an uncontrollable
temper; and his devotion to scientific truth as he saw it being literally passionate, he was an
implacable enemy of those whom he judged guilty of propagating error.
He had other strengths and weaknesses too: - As a penetrating thinker Fisher was
outstanding; but his writings are difficult for many readers. Indeed, some of his teachings
have been most effectively conveyed by the books of others who have been able to simplify
their expression. As a lecturer also, Fisher was too difficult for the average student; his
classes would rapidly fall away until only two or three students who could stand the pace
remained as fascinated disciples. Nor was he particularly successful as an administrator; he
perhaps failed to appreciate the limitations of the ordinary man. But with his wide interests
and penetrating mind he was a most stimulating and sympathetic conversationalist.
R. A. Fisher and Modern Statistics
Introduction
Ronald Fisher undoubtedly laid the foundation for modern statistical methods and their
application. His work contributed to statistics to become and develop in an independent
scientific discipline. His work on statistical inference on the basis of small sample and the
design of experiments is considered outstanding. At the beginning Fisher's work was a little
accepted anywhere except England. In the 1950s American academic statisticians were more
impressed by the work of Neyman and Wald. Later on, Bayesian statistics was drawing more
attention in the specific field of application. In the latter part of the 20th century Fisher's
influence was overshadowed by the introduction of computers in statistics. However, his
work had numerous followers and the number of critics were not insignificant. As
distinguished from many other theorists, he was strongly attached to the statistical
application. Statistical thought has continued to develop by the introduction of innovations in
the theory and application. Many scientists, aware of the deficiency in Fisher's methods,
made an effort to make them better by relying on new scientific achievements.
Generally speaking, Fisher's ideas still have a strong impact on statistical theory. Efron
(1998) and some other authors speculated about the future of Fisherian statistics in the light
of new technological era.
Recent development
A great contribution of R. A. Fisher is the development of likelihood as a fundamental
concept of making inference about the state of system based on the outcome of a set of
experiments of trials. Nowadays, computationally intensive algorithms make possible wider
application of this method and the development of new techniques. Expectation
Maximization (EM) iterative algorithm is a statistical technique for maximizing complex
likelihood and handling incomplete data problem developed by Dempster et al. (1977). It
may be successfully applied in solving Genomic example (Fisher et Balmukand, 1928) it may
be applied in estimation mixtures of distributions that occur in many modern areas as pattern
recognition and data mining. Also, many problems of classification may be converted to
estimation problem. Fisher’s papers on discriminant analysis inspired Anderson to research in
the area of Multivariate analysis and to write his famous book (1984 ).
3. Extreme value theory
Extreme value theory (EVT) (Embrechts et al., 1997, Mladenovi_, 2002) has been one of the
most quickly developing areas of mathematical statistics in the last decades. EVT deals with
asymptotic behaviour of extreme order statistics of a random sample, such as the maximum
and the minimum. It has found many applications in different are as: engineering, material
strength, oceanography, hydrology, pollution studies, meteorology, financial econometrics,
especially in risk management and computation of Value at Risk.
Most statisticians aim to characterize typical behaviour and focus on the center of data. EVT
aims to characterize rare events and tails of distribution. The theorem of Fisher and Tippett
(1928) is the core of this theory. The assertion of this theorem is “limiting forms of the largest
and the smallest observation in a sample of given size are few and comparatively simple,
although with a normal distribution they are approached exceedingly slowly”. Fisher deduced
the possible limiting forms from the functional relation which they must satisfy. The theorem
suggests that asymptotic distribution of the maximum belongs to one of three distributions
regardless of the original data:
(1) G1(x) exp(ex ) , -x ,
(2) G2(x) exp(x) , x 0 , 0 ,
(3) G3(x) exp((x)) , x 0, 0 .
Extreme value distribution G1(x) is Gumbel distribution that has a right tail no thicker than
exponential distribution; G2(x) is Fréchet distribution that exhibits the right tail that declines
by a power and G3(x) is Weibul distribution with finite upper limit. Gnedenko (1943)
continued Fisher’s research in this area and made EVT more rigorous by giving necessary
and sufficient conditions for weak convergence of order statistics. Nowadays modelling
extreme events through heavy-tailed distributions attracts more and more attention. The
number of statisticians working in extreme value methodology and its application, and the
number of publications in this area are growing.