Figures from the History of Probability and Statistics
John Aldrich, University of
Southampton, Southampton, UK. (home)
Notes on the work of
A further 200+ individuals are mentioned below. Use Search on your browser to find the person you are interested in. It is also worth searching for the ‘principals’ for they can pop up anywhere.
The entries are arranged chronologically, so the document can be read as a story. These are the date markers
with people placed according to
date of their first impact. Do not take the placings too seriously and remember
that a career may last more than 50 years! At
each marker there are notes on developments in the following period. There is
more about
For further on-line information there are links to
· Earliest Uses (Words and Symbols) for details (particularly detailed references) on the topics to which the individuals contributed. (The Words site is organised by letter of the alphabet. See here for a list of entries)
· MacTutor for fuller biographical information on the ‘principals’ (all but three) and on a very large ‘supporting’ cast. The MacTutor biographies also cover the work the individuals did outside probability and statistics. The MacTutor and References links are to these pages. There is an index to the Statistics articles on the site.
· ASA Statisticians in History for biographies of mainly recent, mainly US statisticians.
· Life and Work of Statisticians (part of the Materials for the History of Statistics site) for further links, particularly to original sources.
· Oscar Sheynin’s Theory of Probability: A Historical Essay An account of developments to the beginning of the twentieth century, particularly useful for its coverage of Continental work on statistics.
· Isaac Todhunter’s classic from 1865 A History of the Mathematical Theory of Probability : from the Time of Pascal to that of Laplace for detailed commentaries on the contributions from 1650-1800. The coverage is extraordinary and the entries are still interesting—even their humourlessness has a certain charm.
·
The Mathematics
Genealogy Project, abbreviated MGP, which
is useful for tracking modern scholars. The PhD degree is a relatively recent
development and in the
· Wikipedia for additional biographies. This is an uneven site but it has some useful articles.
The entries contain references to the following histories and books of lives. See below for more literature.
·
Ian Hacking The
Emergence of Probability,
·
Stephen M Stigler The
History of Statistics: The Measurement of Uncertainty before 1900,
·
Anders Hald A History of
Probability and Statistics and their applications before 1750,
·
Anders Hald A History of
Mathematical Statistics from 1750 to 1930,
·
Jan von Plato Creating
Modern Probability,
·
Leading Personalities in Statistical Sciences from the Seventeenth
Century to the Present, (ed. N. L. Johnson and S. Kotz) 1997.
·
Statisticians of the
Centuries (ed. C. C. Heyde and E. Seneta) 2001.
·
Encyclopedia of Social
Measurement (ed. K. Kempf-Leonard) 2004.
On the web (see also online biblios and texts below)
· Stochastikon Encyclopedia. Articles in English and German.
· Portraits of Statisticians on the Materials for the History of Statistics site.
· Sources in the History of Probability and Statistics by Richard J. Pulskamp.
· Tales of Statisticians. Vignettes by E. Bruce Brooks.
·
History
of Statistics and Probability 18 short biographies from
· Glimpses of the Prehistory of Econometrics. Montage by Jan Kiviet.
·
Probability
and Statistics Ideas in the Classroom: Lesson from History.
Comments on the uses of history by D.
· The History of Statistics in the Classroom. Thumbnail sketches of Gauss, Laplace and Fisher by H. A. David.
· Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. Encyclopaedic coverage by M. Friendly & D.J. Denis.
·
Actuarial
History. A very
comprehensive collection of links, created by Henk Wolthuis, not only to actuarial science and
demography, but to statistics as well.
To help place individuals I have used modern terms for occupation (e.g. physicist or statistician). For the earlier figures these terms are anachronistic but, I hope, not too misleading. I have not given nationality as people move and states come and go. MacTutor has plenty of geographical information.
1650-1700 The origins of probability and statistics are usually found
in this period, in the mathematical treatment of games of chance and in the
systematic study of mortality data. This was the age of the Scientific
Revolution and the biggest names, Galileo
(Materials
and Todhunter
ch.I (4-6).) and Newton
(LP) gave some thought to probability without apparently
influencing its development. For an introduction to the Scientific
Revolution, see Westfall’s Scientific
Revolution (1986).
·
There
were earlier contributions to probability, e.g. Cardano
(1501-76) gave some ‘probabilities’ associated with dice throwing, but a
critical mass of researchers (and results) was only achieved following
discussions between Pascal
and Fermat
and the publication of the first book by Huygens. Hacking Chapters
1-5 discusses thinking before Pascal. James Franklin’s The Science of Conjecture:
Evidence and Probability Before Pascal (2001) examines this earlier
work in depth. A recent issue of the JEHPS is devoted to Medieval
probabilities.
·
Statistics
in the form of population statistics was created by Graunt. Graunt’s friend William Petty
gave the name Political Arithmetic
to the quantitative study of demography and economics. Gregory King
was an important figure in the next generation. However the economic line
fizzled out. Adam Smith, the most influential C18 British economist,
wrote, “I have no great faith in
political arithmetic...” Wealth of Nations (1776) B.IV,
Ch.5, Of Bounties.
·
A form of life insurance mathematics was developed from Graunt’s work on the life table by the
mathematicians Halley,
Hudde
and de
Witt. Many later ‘probabilists’ wrote on actuarial matters,
including de Moivre, Simpson,
Price, De
Morgan, Gram,
Thiele,
Cantelli,
Cramér and de
Finetti. In the C20 the Skandinavisk aktuarietidskrift and the Giornale dell'Istituto Italiano degli
Attuari were important journals for
theoretical statistics and probability. Actuarial questions and
friendship with the actuary G.
J. Lidstone stimulated the Edinburgh mathematicians, E.
T. Whittaker and A.
C. Aitken (MGPP),
to contribute to statistics and numerical
analysis. The C17 work is discussed by
Hacking (1975): Chapter
13, Annuities. See also Chris Lewin’s The Creation of
Actuarial Science and the other historical links on the International
Actuarial Links
page. There are historical articles in the Encyclopedia of Actuarial Science.
Classics are reprinted in History
of Actuarial Science. There is a nice review of the early
literature in the catalogue
of the Equitable Life Archive.
·
New
institutions,
rather than the traditional universities, underpinned these developments. In
Life & Work has links to the writings of many of these people. For the period generally see Todhunter ch. I-VI (pp. 1-55) and Hald (1990, ch. 1-12).
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Blaise Pascal (1623-1662) Mathematician and philosopher. MacTutor References SC, LP. Pascal
was educated at home by his father, himself a considerable mathematician. The
origins of probability are usually found in the correspondence
between Pascal and Fermat where they treated several problems associated
with games of chance. The letters were not published but their contents were
known in Parisian scientific circles. Pascal’s only probability publication
was the posthumously published Traité du
triangle arithmétique (1654, published in 1665 and so after Huygens’s work); this treated Pascal’s
triangle with probability
applications. Pascal introduced the concept of expectation and discussed the problem of gambler’s
ruin. Pascal’s
wager, is now often read as a pioneering analysis of
decision-making under uncertainty although it appeared, not in his
mathematical writings, but in the Pensées, his reflections on
religion. The last chapter of the Port-Royal
Logic pp.
365ff by Pascal’s friends Arnauld
and Nicole has a brief treatment of the use of probability in decision making,
with an allusion to the wager. See Ben Rogers Pascal's
Life & Times, Life
& Work, A.W.F.
Edwards on the triangle and Todhunter
ch.II (pp. 7-21). See also Hald 1990, chapter 5, The
Foundations of Probability Theory by Pascal and Fermat in 1654 and Hacking
1975, chapter
7, The |
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Christiaan
Huygens (1629-94) Mathematician and physicist. MacTutor
References SC, LP. As a youth Huygens was expected
to become a diplomat but instead he became a gentleman scientist, making
important contributions to mathematics, physics and astronomy. He was educated at the |
)
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No authentic portrait of Graunt is known |
John Graunt (1620-74) Merchant. Wikipedia. SC, LP, ESM. Graunt is unique among the figures described here in
not having had a university education. He published only one work, Observations
Made upon the Bills of Mortality (1662). However, through
this work and his friendship with William Petty,
he became a fellow of the Royal Society of London and his work became known
to savants like Halley.
The weekly bills of mortality, which had been collected since 1603, were
designed to detect the outbreak of plague. Graunt
put the data into tables and produced a commentary on them; he does basic
calculations. He discusses the reliability of the data. He compares the
number of male and female births and deaths. In the course of Chapter XI on
estimating the population of London Graunt produces a primitive life table see the JIA
articles by Glass, Renn, Benjamin and Seal. The life table became one of the
main tools of demography and insurance mathematics. Halley produced a life
table using data from Caspar
Neumann (SC) in |
1700-50
The great leap forward
is Hald’s (1990) name for the decade 1708-1718: there were so many important
contributions to such a greatly expanded subject. The roots of probability and
statistics were quite distinct but by the early C18 it was understood that the
subjects were closely related.
·
Jakob Bernoulli’s Ars Conjectandi, like Arnauld’s
Logique (1682) pp.
365ff, suggested a conception of probability broader than that
associated with games of chance. Bernoulli’s
law of large numbers
provided a theory to link between probability and data. See Hacking
(1975): Chapters
16-7.
·
Montmort’s
(SC, LP) Essay
d'analyse sur les jeux de hazard (1708) and de Moivre’s Doctrine of
Chances (1718) produced many new results on games of chance, greatly
extending the work of Pascal
and Huygens.
·
Arbuthnot’s (SC, LP) 1710 paper An Argument
for Divine Providence, taken from the constant Regularity observed in the
Births of both Sexes used a significance test (sign test) to establish
that the probability of a male birth is not ½. The calculations were refined by
'sGravesande (LP)
and Nicholas
Bernoulli (LP). Apart from being an early application of probability
to social statistics, Arbuthnot’s paper illustrates the close connection
between theology
and probability
in the literature of the time. The work of John
Craig provides another example.
·
Consideration
of the valuation of a risky prospect, dramatised by the St. Petersburg
paradox (formulated by Nicholas
Bernoulli in 1713 and discussed by Gabriel
Cramer) led to Daniel Bernoulli’s (1737)
theory of moral expectation (or expected utility).
See Life & Work for writings by Montmort, Euler, Lagrange, etc. For the period see Todhunter ch. VII-X (pp. 56- 212) Hald (1990, ch. 1-12), Hacking Chapter 16-9.
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Jakob (James) Bernoulli (1654-1705)
Mathematician. MacTutor
References SC, LP, ESM. Eight members of the Bernoulli family have
biographies in MacTutor
(family
tree) and several wrote on probability. The most important
contributors were Jakob, Daniel and Niklaus.
Jakob and his younger brother Johann
were the first of the mathematicians. Jakob studied philosophy at the |
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Abraham de Moivre (1667-1754) Mathematician MacTutor References SC, LP. De Moivre came to |
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Daniel Bernoulli (1700-1782) Mathematician and physicist MacTutor References SC, LP. Daniel
Bernoulli, a nephew of Jakob Bernoulli, was educated at the
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1750-1800 Probability
established itself in physical science, in astronomy its most developed branch. The most enduring
of these applications to astronomy treated the combination of observations. The resulting theory of errors was the most important ancestor of modern
statistical inference, particularly of estimation theory.
·
The
major mathematician/astronomers, including Daniel Bernoulli, Boscovich,
Euler,
Lambert,
Mayer
and Lagrange,
treated the problem of combining astronomical observations, “in order to
diminish the errors arising from the imperfections of instruments and the
organs of sense” in the words of Thomas
Simpson. Simpson introduced the idea of postulating an error distribution. See Hald (1998, Part I Direct
Probability, 1750-1805) and Richard J. Pulskamp’s Sources in the History of
Probability and Statistics.
·
More
tests of significance
were developed, mainly for use in astronomy, see Daniel Bernoulli
and also John
Michell (1767) Crossley, who calculated the odds that the
Pleiades is a system of stars and not a random agglomeration. See Hald
(1998): Part I Direct Probability, 1750-1805).
·
Interval
statements about the parameter of the Binomial distribution—ancestors of the
modern confidence
interval—were produced by Lagrange and Laplace in the 1780s.
·
In
the 1770s Condorcet
started publishing on social mathematics, largely the application of
probability to the decisions of juries and other assemblies. His work had a
strong influence on Laplace and Poisson. Other French authors from this period included D’Alembert
and Buffon;
the former is best remembered for his critical remarks on probability and the
latter for his needle experiment.
·
An important development in
probability theory was work on conditional
probability with applications to inverse probability or Bayesian inference by
Bayes and Laplace. See Hald
(1998): Part II Inverse Probability.
See Todhunter ch. XI-XIX and Stigler (1986): Part I, The Development of Mathematical Statistics in Astronomy and Geodesy before 1827. For this period and the next see also Lorraine Daston (1988) Classical Probability in the Enlightenment.
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No authentic portrait of Bayes is known (for an unlikely possibility see here) |
Thomas Bayes (1702-1761) Clergyman and mathematician. MacTutor
References SC, LP, ESM. Bayes
attended the |
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Pierre-Simon Laplace (1749-1827) Mathematician and physicist MacTutor
References SC, LP, ESM. |
1800-1830 The contrasting
figures of Laplace and Gauss dominate this period.
·
Work on the theory of errors reached a climax
with the introduction of the method
of least squares. The method was published by Legendre
in 1805 and within twenty years there were three probability-based
rationalisations, Gauss’s Bayesian argument (see uniform prior), Laplace’s argument based on the central limit theorem
and Gauss’s Gauss-Markov
theorem. Work continued through the C19 with numerous mathematicians and
astronomers, contributing, including Cauchy
(Cauchy distribution), Poisson,
Fourier,
Bienaymé,
Bessel
(probable error), Encke, Peters
(Peters' method), Lüroth,
Robert Ellis,
Airy,
Glaisher,
Chauvenet
and Newcomb. (The Cauchy distribution
first appeared as an awkward case for the theory of errors.) Pearson, Fisher
and Jeffreys were taught the theory of errors by
astronomers. In the C20 astronomers, including Eddington,
Kapteyn
and Charlier,
also investigated the statistical properties of constellations, picking up from
the middle of the C18. (above)
·
Gauss found a second important
application of least squares in geodesy. Geodesists
made important contributions to least squares, particularly on the
computational side—not surprisingly as the calculations could be on an
industrial scale. The eponyms, Gauss-Jordan
and Cholesky MacTutor,
honour later geodesists. Helmert
(Helmert's transformation)
and Paolo Pizzetti
were geodesists who contributed to the theory of errors. At least one
important C20 statistician started as a surveyor, Frank
Yates, Fisher’s colleague and successor at
Rothamsted.
·
In
·
Around this time William Playfair
was finding new ways of representing data graphically but nobody was paying
attention. Techniques slowly accumulated over the next 150 years without the
idea of graphical statistics as a study in its own right gaining ground. That
idea is quite recent and mainly associated with Tukey. See
Milestones.
·
The age of the academies
was over and from now on the main advances took place in universities. The
French education system was transformed in the course of the Revolution and the
C19 saw the rise of the German university.
See Stigler (1986): Part
I, The Development of Mathematical Statistics in Astronomy and Geodesy before
1827 and Hald (1998): Part III The Normal Distribution, the
Method of Least Squares and the Central Limit Theorem. See
Life
& Work. See also L. Daston (1988) Classical
Probability in the Enlightenment.
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Carl Friedrich Gauss (1777-1855)
Mathematician, physicist and geodesist.
MacTutor
References SC, LP. Gauss is generally regarded
as one of the greatest mathematicians of all time and his contributions to
the theory of errors
were only a small part of his total output. Gauss spent most of his working
life at the |
1830-1860 This
period saw the emergence of the statistical society, which has been on
the stage ever since, although the meaning of “statistics” has changed and the
beginning of a philosophical literature on probability. It saw also the
beginning of the most glamorous branch of empirical time series analysis, the
sunspot cycle.
·
Since the 1830s there have
been statistical societies, including the London
(Royal) Statistical Society Wikipedia
and the American
Statistical Association (now the world’s largest). The Statistical Society of Paris
was founded in 1860. The International
Statistical Institute Wikipedia
was founded in 1885 although there had been international congresses from 1853.
Statistics were
facts about human populations and in
·
Since 1840, or so, there
has been a philosophical literature on probability. The English
literature begins with the extensive discussion of probability in John Stuart
Mill’s System of Logic (1843). This was followed by The
Logic of Chance (1862) of John
Venn, the Principles of Science (1873) of W. Stanley Jevons
and the Grammar of Science (1892) of Karl Pearson.
The American scientist/philosopher C.S.
Peirce (Stanford)
wrote extensively on probability, although he was not much read. There was an
overlapping literature on logic and probability.
De
Morgan can be placed here as well as Boole
(LP) whose An Investigation into the
Laws of Thought, on which are founded the Mathematical Theories of Logic and
Probabilities (1854) contained a long discussion of probability. Later
figures are mentioned below. There were German and French
literatures as well but philosophical probability was less international than
mathematical probability. See Porter’s Rise of Statistical
Thinking.
·
In 1843 Schwabe observed that sunspot activity is periodic. There followed
decades of research, not only in solar physics but in terrestrial magnetism,
meteorology and even economics examining series to see if their periodicity
matched that of the sunspots. Even before the sunspot craze there was intense
interest in periodicity in meteorology, tidology, and other branches of observational physics and, by
the end of the century seismology, was becoming important. Both Laplace and Quetelet had analysed meteorological
data and Herschel had written a book on the
subject. The techniques in use varied from the simple, such as the Buys
Ballot table, to the sophisticated, forms of harmonic
analysis.
At the end of the century the physicist Arthur Schuster
introduced the periodogram.
However, by then a rival form of time series analysis, based on correlation
and promoted by Pearson, Yule, Hooker
and others, was
taking shape. For an account see J. L. Klein (1997) Statistical
Visions in Time,
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Lambert Adolphe Jacques Quetelet (1796-1874)
Astronomer and statistician. MacTutor
References
SC, LP, ESM. Adolphe Quetelet studied at the |
)
1860-1880 Two
important applied fields opened up in this period. Probability found a
major new application in physical science, to the theory of gases, which
developed into statistical mechanics. Problems in statistical mechanics were behind many
of the probability advances of the early C20. The statistical study of heredity developed into
biometry and many of the advances in statistical theory
were associated with this subject. There were important geographical
changes, as important work in probability
started to come from
·
In 1860 James
Clerk Maxwell used the error curve (normal distribution) in the
theory of gases; he seems to have been influenced by Quetelet via
John
Herschel’s review of the Letters on Probability. Boltzmann and Gibbs
developed the theory of gases into statistical
mechanics.
·
Galton
inaugurated the statistical study of heredity,
work continued way into the C20 by Pearson and Fisher.
Correlation was the most distinctive contribution of this “English” school. See
Stigler (1986): Part III, A Breakthrough in Studies of Heredity.
·
By contrast, the so-called
“continental direction” investigated the appropriateness of simple urn models
for treating birth and death rates by considering the stability of the series
of rates over time. Wilhelm Lexis Theorie der Massenerscheinungen
in der menschlichen Gesellschaft (1877). Bortkiewicz Markov Chuprov and Anderson all worked in this tradition. See Stigler
(1986): Chapter 6, Attempts to revive the Binomial, C. C. Heyde & E.
Seneta I. J. Bienaymé: Statistical Theory Anticipated, 1977 and Sheynin ch. 15.1.
·
‘Higher’ statistics entered
psychology and economics.
For psychology see Fechner. In economics W. Stanley Jevons
(Wikipedia
MacTutor
New School)
(SC) saw himself as continuing the work of the political
arithmeticians of 1650+. In the intervening two centuries
much had been done and Jevons’s work on index numbers was
inspired by the theory of errors, while his research on economic time series
was inspired by the work of meteorologists on seasonal variation and of
physicists on the solar cycle and its terrestrial correlates. (see above) Jevons also tried to link his mathematical economic
theory (see utility)
to statistical analysis—a project revived in the econometrics of the C20.
See Stigler (1986) and T. M.
Porter The Rise of Statistical Thinking 1820-1900 (1986).
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Ludwig Boltzmann (1844-1906)
Physicist. MacTutor
References.
MGP.
LP. Boltzmann, with Gibbs,
was responsible for transforming Maxwell’s
probabilistic theory of gases into statistical mechanics. Boltzmann was
awarded a doctorate from the |
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Gustav Theodor
Fechner (1801-1877) Wikipedia Physicist and psychologist. SC. Fechner went to the |
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Francis Galton (1822-1911) Man of science MacTutor
References
SC, LP, ESM. After studying mathematics at |
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P. L. Chebyshev (1821-94) Mathematician.
MacTutor
References.
SC, LP. Chebyshev was
one of the most important of C19 mathematicians and probability formed only a
small part of his output. He had predecessors in |
)
1880-1900 In this period the English statistical school
took shape. Pearson was the
dominant force until Fisher displaced
him in the 1920s. The school dominated statistics until the Second World War.
T. Schweder’s Early Statistics in the Nordic Countries considers
why this did not happen in
·
Galton introduced correlation and a
theory was rapidly developed by Pearson, Edgeworth, Sheppard and Yule. Correlation was major departure from the statistical
work of Laplace and Gauss, both as a technique and because of the applications
it made possible. It became widely used in biology, psychology and social
science.
·
In economics Edgeworth developed
some of Jevons’s ideas, most
notably on index numbers. However, economic statistics in
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F. Y. Edgeworth (1845-1926) Economist and
statistician. MacTutor
References.
SC, LP, ESM. Edgeworth studied classics at
Trinity College Dublin and Balliol College Oxford. From around 1880 he
followed dual careers in economics and in statistics. Edgeworth seems to have
been self-taught in mathematics and he made a thorough study of the subject
and remained very well read. He began in statistics by subjecting the casual
statistical methods of Jevons to rigorous examination and started what turned
out be made a long involvement with index numbers (see
“Money” in his Papers
relating to Political Economy, vol. 2). However, most of his
extensive publications in statistical theory were not motivated by
economic applications, or direct applications of any kind. In 1892
Edgeworth, prompted by Galton, examined correlation and
methods of estimating correlation coefficients. Another concern, which led to
a stream of papers, was with generalisations of the normal distribution, as
in e.g. his 1905 paper “The law of error”. The Edgeworth expansions
that came from this research are now associated with distributions of
estimators and test statistics but Edgeworth originally envisaged these
distributions used for data distributions, as an alternative to the Pearson curves.
Edgeworth’s starting point was Laplace. Much of his work
was not followed up, like his 1908/9 papers “On the probable errors of
frequency-constants” which anticipated some of Fisher’s large sample theory for maximum likelihood.
Unlike his contemporaries, Pearson in statistics and Alfred Marshall in
economics, Edgeworth founded no school. From 1891 he was professor of
political economy at |
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Karl Pearson (1857-1936)
Biometrician, statistician & applied mathematician. MacTutor
References.
SC, LP, ESM. Karl Pearson read mathematics at |
1900-1920 In the years before the Great War of 1914-18 probability and statistics were expanding in all directions. During the war research in statistics and probability almost stopped as people went into the armed services or did other kind of war work. Pearson, Lévy and Wiener worked in ballistics, Jeffreys in meteorology and Yule in administration. For the mathematicians’ traditional role in war, see The Geometry of War.
·
In
1900 David
Hilbert proposed a set of problems
for the C20. The 6th was, “to treat … by means of axioms,
those physical sciences in which mathematics plays an important part; in the
first rank are the theory of probabilities and mechanics.” Measure
theory which would have a key
role in the axiomatisation of probability was being created by Borel, Lebesgue
and others—see below.
·
From different subjects
came contributions that eventually found a place in the theory of stochastic
processes. In physics Einstein
and Smoluchovski
(see Cohen’s
History of Noise) worked on Brownian motion. Bachelier
(see Bru
& Taqqu) developed a similar model applied to financial
speculation—that application was a sleeper until the 1970s.
The actuary Lundberg developed a theory of collective risk. Malaria and the migration of mosquitoes were
behind Pearson’s interest in the random walk problem.
Mathematical models of epidemics were developed
by Ronald Ross
and A. G.
McKendrick MacTutor
without reference to the earlier work of Daniel Bernoulli.
·
Mendel did not use probability in his work on genetics
(published 1866) but his ideas were
probabilised as Pearson, Yule and Fisher
investigated how far his principles could rationalise the findings of the
biometricians.
·
Correlation began to be
important in psychology, largely through Charles Spearman
(1863-1945). Amongst his contributions to statistics were rank correlation and factor analysis. Godfrey Thomson
was a severe critic of Spearman’s factor analysis of intelligence. In the 1930s
Louis L.
Thurstone developed a multiple factor analysis.
·
In economics,
especially in the
·
Industrial
applications of probability begin
with Erlang’s
work on congestion in telephone systems, the ancestor of modern queuing theory
·
Institutional
developments include the creation in 1911 of the Department of Applied Statistics at UCL
headed by Pearson. Also in
See Hald (1998, Part IV)
and von Plato (ch. 3) “Probabilities in Statistical Physics.” For
developments in economics see M. S. Morgan A History of Econometric Ideas,
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G. Udny Yule (1871-1951) Statistician. MacTutor
References.
Wikipedia |
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A. A. Markov (1856-1922) Mathematician. MacTutor References. SC, LP. Markov spent his working life at the University of St. Petersburg. Markov was, with Lyapunov, the most distinguished of Chebyshev’s students in probability. Markov contributed to established topics such as the central limit theorem and the law of large numbers. It was the extension of the latter to dependent variables that led him to introduce the Markov chain. He showed how Chebyshev’s inequality could be applied to the case of dependent random variables. In statistics he analysed the alternation of vowels and consonants as a two-state Markov chain and did work in dispersion theory. Markov had a low opinion of the contemporary work of Pearson, an opinion not shared by his younger compatriots Chuprov and Slutsky. Markov’s Theory of Probability was an influential textbook. Markov influenced later figures in the Russian tradition including Bernstein and Neyman. The latter indirectly paid tribute to Markov’s textbook when he coined the term Markoff theorem for the result Gauss had obtained in 1821; it is now known as the Gauss-Markov theorem. J. V. Uspensky’s Introduction to Mathematical Probability (1937) put Markov’s ideas to an American audience. See Life & Work There is an interesting volume of letters, The Correspondence between A.A. Markov and A.A. Chuprov on the Theory of Probability and Mathematical Statistics ed. Kh.O. Ondar (1981, Springer) See also Sheynin ch. 14 and G. P. Basharin et al. The Life and Work of A. A. Markov. |
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‘Student’ = William Sealy Gosset (1876-1937)
Chemist, brewer and statistician. MacTutor
References.
Wikipedia
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1920-1930 Many of the people who would dominate probability and
statistics over the following decades, first made an impact. Of them, the
individual who had the greatest hold over his subject was Fisher
in statistics. The ascendancy of Fisher was also the ascendancy of the
English language. While German was the international scientific language of the
time—and the language of probability—Fisher and his followers rarely referred
to literature in German, believing that that literature ended with Gauss, although Helmert
was later added to the canon. Thus standard works, like those by Czuber,
did not cross the Channel.
·
In probability advances included refinements of the central limit theorem
(here Lindeberg
made an important contribution) and the strong law of large numbers
(which went back to Borel
in 1909 and Cantelli
in 1917) and new results including the law of the iterated logarithm.
There were contributions from most countries of Continental Europe, e.g. Mazurkiewicz
from
·
The
foundations of probability received much
attention and certain positions found classic expression: the logical
interpretation of probability (degree of reasonable belief) was propounded by
the Cambridge philosophers, W.
E. Johnson, J.
M. Keynes and C.
D. Broad, and presented to a scientific audience by Jeffreys; Keynes was influenced by the German
physiologist/philosopher J. von Kries.
The frequentist
view was developed by von Mises.
·
The Modern (Evolutionary)
Synthesis of Mendelian genetics
and Darwinian natural selection involved the solution of problems involving
stochastic processes, e.g. branching
processes. However, the work
did not have as much influence on the development of probability theory as
similar work in physics; see Fokker-Planck
equation. The
principal contributors to the modern synthesis,
Fisher, J. B. S. Haldane
and Sewall
Wright (path
analysis), all contributed to statistics, but Fisher was in a class
apart.
·
In statistics
R. A. Fisher generated many new ideas on estimation and hypothesis testing and
his work on the design of
experiments moved that topic from the fringes of statistics to the centre. His Statistical Methods for
Research Workers (1925)
was the most influential statistics book of the century.
·
W.
A. Shewhart ASQ Wikipedia
pioneered quality control, which
became a major industrial application of statistics.
See Hald (1998, ch. 27 and passim) and von Plato (ch. 4-6)
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By permission of Fisher Memorial Trust |
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Paul Lévy (1887-1971) Mathematician.
MacTutor
References.
MGP.
LP. In the late C19 French
mathematicians continued to work on probability but Bertrand
and Poincaré
made no advances comparable to those made by Laplace and his
contemporaries, nor did they conserve the rich tradition. Major
mathematicians, including Borel
(see normal number)
and Fréchet, wrote on probability in the early C20 but Lévy became
the leading French probabilist. Lévy was originally interested in analysis
(see functional analysis)
and he only started publishing on probability around 1920. In 1920 Lévy was
appointed Professor of Analysis at the École Polytechnique, a position he
held until 1959. He revived characteristic
function methods (the name is his) and used them in his work on the stable laws and the central limit theorem.
This work was summarised in his influential Calcul des Probabilités (1925).
In the 1930s he focussed on the study of stochastic processes, in particular martingales and Brownian motion. Théorie de l'addition des variables
aléatoires (1937) Processus
stochastiques et mouvement brownien (1948). See also Annales
(including nice photos) and Rama Cont. See also von Plato passim. Paul Lévy,
Maurice Fréchet : 50 ans de correspondance
mathématique (eds. Barbut,
Locker & Mazliak) includes
a review of Lévy’s work in probability.
Lévy’s student Michel Loève moved to |
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Richard von Mises (1883-1953) Applied
mathematician. MacTutor.
References. MGP.
SC, LP. Mises was educated at the
Technische Hochschule in |
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Harold Jeffreys (1891-89) Applied mathematician and physicist. MacTutor
References.
SC, LP. Jeffreys has a good claim to be
considered the first Bayesian statistician in that he used only Bayesian methods. Jeffreys
arrived to study mathematics at |
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Norbert Wiener (1894-1964) Mathematician.
MacTutor
References.
MGP.
SC, LP. Wiener’s working life was spent
at MIT. He was well-travelled, having studied at Harvard, |
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Aleksandr
Yakovlevich Khinchin (1894-1959)
Mathematician. MacTutor
References
MGP Publications.
Khinchin was a student at Moscow State University
and spent almost all his working life there. Khinchin, like Lévy
and Doob, started in analysis. The university had a very
strong analysis group and Khinchin’s supervisor was Luzin.
There was no tradition of work in probability until, that is, Khinchin and Kolmogorov created one. There do not seem to have been any
personal links with the Chebyshev/Markov
tradition at |
)
1930-1940 Against a calamitous economic and political background there were important developments in probability, statistical theory and applications. In the Soviet Union mathematicians fared better than economists or geneticists and in the early years they could travel abroad and publish in foreign journals; thus Kolmogorov and Khinchin published in the main German periodical, Mathematische Annalen GDZ. In Germany Jews were barred from academic jobs from 1934.
·
In probability
the main developments were Kolmogorov’s axiomatisation of probability and the
development of a general theory of stochastic
processes by him and Khinchin. This work is
usually seen as marking the beginning of modern probability. See von Plato (ch. 7) “Kolmogorov’s measure
theoretic probabilities.” Most of the activity was in the Soviet Union and
·
In the foundations of probability Bruno de
Finetti and Frank Ramsey’s (1903-1930) (St.
Andrews, N.-E.
Sahlin) work on subjective probability appeared. Ramsey started by
criticising the
·
In
·
In statistical
inference the main development was the Neyman-Pearson theory of hypothesis testing from
1933 onwards. Multivariate analysis
became an identifiable subject, formed out of such contributions as the Wishart distribution
(1928), Harold
Hotelling’s principal
components (1933) and canonical
correlation (1936) and Fisher’s discriminant analysis
(1936).
·
Applications of mathematics
and statistics to economics came together in the
econometric
movement. This could look back to the C17 political arithmetic and the C19 work
on index numbers
and on Pareto's law
but econometric modelling, which involved the application of regression methods to
economic data, was a C20 development. Among the leaders in the 1930s were Jan
Tinbergen and Ragnar
Frisch. Econometricians who have been followed them as Nobel laureates
in economics include Engle, Granger, Haavelmo, Heckman, Klein, McFadden. Equally important were developments in the
collection of economic information. In the
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Andrei
Nikolaevich Kolmogorov (1903-87) Mathematician. MacTutor
References.
MGP.
LP. Kolmogorov was one of the most
important of C20 mathematicians and although he wrote a lot of probability it
was only a small part of his total output. Like Khinchin,
he was a student of Luzin
at |
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Jerzy Neyman (1894-1981) Statistician. MacTutor
References.
NAS
ASA
MGP.
SC, LP, ESM. Neyman was educated in the tradition of Russian
probability theory and had a strong interest in pure mathematics. His
probability teacher at |
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Harald Cramér (1893-1985) Mathematician,
statistician & actuary. MacTutor
References.
MGP.
Photos SC, LP. Personal
recollections Statistical
Science 1986. Cramér
studied at the |
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Bruno de
Finetti (1906-85) Mathematician, actuary & statistician. MacTutor
References
Wikipedia
LP. De Finetti studied mathematics in |
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William
Feller (1906-70) Mathematician. MacTutor
References.
MGP.
About half of Feller’s papers were in probability, the rest were in
calculus, functional analysis and geometry. After a first degree at the |
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J. L. Doob
(1910-2004) Probabilist. MacTutor
References.
MGP. SS
Interview. Because Wiener was not part
of the probability community, Doob was the first “modern probabilist” from
the |
1940-1950 Among the millions who died in the Second World War
were mathematicians and statisticians. Doeblin
is only the best known of those killed; one of Neyman’s books
is dedicated to 10 lost colleagues and friends. Yet
this war, unlike the First World War, promoted the study of statistics and
probability. At the end of the war there were many more people working in
statistics, there were new applications and the importance of the subject to
society was more widely recognised.
·
The Nazi persecutions and
the Second World War drove many statisticians and mathematicians to the
·
The war brought many people
into statistics and probability. Savage and Tukey
are examples from the US while in Britain the recruits included Barnard
(MGP),
Box (MacTutor)
(MGP), Cox
(MGP),
D.
G. Kendall (MGP),
Lindley
(MGP).
The recruits were often better trained in abstract mathematics than earlier
statisticians. This contributed to closing the gap between the English
statistical and the Continental probability traditions.
·
The war generated research
problems out of which came Wiener’s
work on prediction and Wald’s on sequential analysis and
the new subject of operations
research. Governments’ need for information led to great expansion
in the production of official statistics. In
·
Between 1943 and –6 three
advanced treatises on statistics appeared, by Cramér, M.
G. Kendall and Wilks
(MGP).
These works did much to consolidate the subject and thereby professionalise it.
·
Nonparametric methods
began to be systematically studied, using tools from the theory of statistical
inference; E. J. G.
Pitman was an important pioneer. The tests often came originally
from non-statisticians, like Spearman (rank correlation) or Wilcoxon
(Wilcoxon tests).
The existing repertoire of sign
test, permutation
test and Kolmogorov-Smirnov
test was soon expanded.
·
Modern time series analysis
came from the union of the theory of stochastic processes (see Khinchin
and Cramér), the
theory of prediction (Wiener and Kolmogorov)
and the theory of statistical inference (Fisher and Neyman) with harmonic analysis and correlation among the
grandparents. (above) One of the
main pioneers of the 40s was M. S. Bartlett.
In the 50s Tukey was a leading contributor, in the 60s Kalman (Kalman filter) and
systems engineers made important contributions and in the 70s the methods of G. E. P. Box Interview
and G. M. Jenkins
(Box-Jenkins) were
adopted in economics and business.
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Abraham Wald (1902-1950)
Statistician. MacTutor
References.
MGP.
LP. Wald studied at the |
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C. R. Rao (b. 1920) Statistician. MacTutor References
ASA MGP.
Recent
photo. Rao is the most distinguished member of the Indian statistical
school founded by P.
C. Mahalanobis and centred on the Indian Statistical Institute
and the journal Sankhya.
Rao’s first statistics teacher at the |
1950-1980 Expansion continued—more
fields, more people, more departments, more books, more journals! Computers began to have an impact—see below for more
details.
·
Existing departments were expanded:
e.g. in 1949 a second chair of statistics was created at LSE filled by M.
G. Kendall. Bowley (above) only ever had a staff
of 2, E. C. Rhodes
and R. G. D. Allen. New institutions were created, e.g. the
Statistical Laboratory at Cambridge in 1947 and the Statistics Department
at Harvard in 1958.
·
The scope of probability theory increased with the emergence of new
sub-fields such as queueing
theory and renewal
theory. Feller’s Introduction to
Probability Theory made a very strong impact on in the English-speaking
world; it promoted the study of the subject and made advanced topics, like Markov chains,
accessible.
·
In 1950 the
logician/philosopher Rudolf
Carnap published a major work, Logical Foundations of
Probability which advanced a dual interpretation of probability, as degree
of confirmation, which looked back to Cambridge (see Jeffreys),
and as relative frequency, which looked back to von Mises.
Probability was an important topic for other philosophers of science, including
Hans Reichenbach
and Karl
Popper. More recently philosophers have been attracted to the
monism of de Finetti’s subjectivism. Alan Hajek’s Interpretations
of Probability in the Stanford Encyclopedia of
Probability reviews the modern scene.
·
In statistics
there was a Bayesian revival. In
·
W.
Edwards Deming (ASQ)
Wikipedia
(LP) continued Shewhart’s work on quality control and was
very effective in getting industry to adopt these methods.
·
There was a great expansion
in medical statistics and epidemiology. Austin Bradford
Hill was an important contributor to both fields: he pioneered randomised clinical trials and, in work
with Richard Doll,
demonstrated the connection between cigarette smoking and lung cancer.
·
Laplace
and Quetelet saw the work of the census as a possible
application of probability but the use of statistical theory by official data
gatherers only became institutionalised through the activities of Morris Hansen
(interview)
at the US Census Bureau.
·
Since
the 50s finance
has been an important area for applied decision theory: the 1990 Nobel Prize in
economics was awarded to Markowitz
for work that was influenced by Savage although the idea of
expected utility goes back to Daniel Bernoulli. Since the 70s
finance has been an important area for applied stochastic processes. Ito had developed his stochastic calculus in
the 40s but it was applied in an unexpected way in the Black-Scholes model for
pricing derivatives. Scholes
and Merton
received the 1997 Nobel Prize in economics for their contribution (see Black-Scholes formula).
The intellectual ancestor of stochastic finance was Bachelier (above).
·
In 1973 the Annals of
Mathematical Statistics (see above) split into the
Annals of Probability and the Annals of Statistics. This represented
increasing specialisation—there were weren’t many new Cramérs—as well as the need to expand journal pages.
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Leonard
Jimmie Savage (1917-71) Statistician. MacTutor
References.
MGP
LP. After training
as a pure mathematician and obtaining a PhD from the |
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John W. Tukey (1915-2000) Statistician. MacTutor
References.
ASA
and Bell Labs.
MGP. Tukey
originally trained as a topologist (see finite character and Zorn's lemma) but
became a statistician in the Second World War. He remained in |
1980+ Instead of describing people from the very recent past, I describe the effect the computer has had on statistics from its advent, around 1950 and the changes in the writing of the history of probability and statistics in recent decades.
The effects of the computer. The changes following the introduction of the computer have been much more radical than those following the increased use of mechanical calculating machines at the end of the C19. Such machines provided the material basis for Pearson and Fisher’s research and for the construction of their statistical tables in the period1900-50. The machines were not in general use and Fisher assumed that most of the users of the tables and the “research workers” who read his book would use logarithm tables or a slide rule. For general background see A Brief History of Computing.
With the availability of
computers old activities took less time and new activities became possible.
·
Statistical tables and
tables of random numbers first became much easier to produce and then they
disappeared as their function was subsumed into statistical packages.
·
Much bigger data sets could
be assembled and analysed.
·
Exhaustive data-mining became
possible.
·
Much more complex models
and methods could be used. Methods have been designed with computer
implementation in mind—a good example is the family of Generalized
linear models linked to the program GLIM; see John Nelder FRS.
·
In the early C20 when Student (1908) wrote about the normal mean and Yule
(1926) about nonsense correlations they used sampling experiments and in the
1920s it became worthwhile to produce tables of random numbers. With the
introduction of computer-based methods for generating pseudo random numbers
much more ambitious Monte-Carlo
investigations (introduced by von
Neumann and Ulam)
became possible. The Monte-Carlo experiment became a standard way of
investigating the finite sample behaviour of statistical procedures.
·
Since around 1980
Writing history. In recent
decades there has been a flood of works—books and articles—on the history of
probability and statistics from statisticians, philosophers and historians. I
will mention a few titles in each category to indicate the range of activity.
·
50 years ago the standard
general works were Todhunter for the history of probability,
Walker
for statistics with an emphasis on psychology and education and Westergaard
for statistics with an emphasis on economic and vital statistics.
Helen M.
Walker (1929) Studies in the History of Statistical Method, Baltimore: Williams &
Wilkins.
Harald
Westergaard (1932) Contributions to the History of Statistics,
·
E
S Pearson got history moving in
F. N. David (1962) Games, Gods and Gambling:
the Origins and History of Probability and Statistical Ideas from the Earliest Times
to the Newtonian Era.
E. S. Pearson
(ed) (1978) The History of Statistics in the 17th and 18th Centuries against
the Changing Background of Intellectual, Scientific and Religious Thought:
Lectures by Karl Pearson given at University College, 1921-1933.
·
Oscar Sheynin, Anders
Hald and Stephen Stigler
(see above) have been the leading contributors to the
technical literature. Sheynin has published many articles, mainly in the
Archive
for History of Exact Sciences. There is a list of Hald’s
history writings here.
Some of Stigler’s articles are reprinted in
Stephen M
Stigler (1999) Statistics on the Table: The History of Statistical Concepts
and Methods,
·
Much
neglected work has been rediscovered. Bienaymé’s
(
C. C. Heyde
& E. Seneta (1977) I. J. Bienaymé: Statistical Theory
Anticipated,
S. L.
Lauritzen (2002) Thiele: Pioneer in Statistics,
A. Hald (1998)
A History of Mathematical Statistics from
1750 to 1930,
·
Among
the philosophers
are Hacking and von Plato; as well as the books referred to above,
see
I. Hacking
(1990) The Taming of Chance
·
In recent decades the history and sociology of science have flourished. T. S.
Kuhn’s Structure of Scientific Revolutions (1962) had a
strong influence on both fields. Among the works on probability and statistics
by historians and sociologists are
T.
M. Porter (1986) The Rise of Statistical Thinking 1820-1900, Princeton:
L. Daston
(1988) Classical Probability in the Enlightenment. Princeton:
The Probabilistic
Revolution, volume 1 edited by L. Krüger, L. J. Daston and M. Heidelberger,
volume 2 edited by L. Krüger, G. Gigerenzer and M. S. Morgan Cambridge, Mass.:
MIT Press (1987) contents
D. A. MacKenzie (1981) Statistics
in
There is a review essay of Daston
and Krüger et al. by MacKenzie in
·
Much
effort has gone into making important texts available
S. M. Stigler and I. M. Cohen American Contributions to Mathematical Statistics in the Nineteenth Century, contents (includes work by Adrain, De Forest, Newcomb, B. Peirce, C.S. Peirce (Stanford) and others)
H. A. David & A. W. F.
Edwards (eds.) (2001) Annotated
·
Post-1940
developments have not attracted the attention of historians yet. Some classic modern
contributions are reprinted (with commentary) in S. Kotz & N. L. Johnson
(Editors) (1993/7) Breakthroughs in
Statistics: Volume I-III New York Springer Amazon.
Statistical Science has been publishing interviews for the past 20 years and
these are a form of living history—there must be 100 by now; the post-1995
issues are available through Euclid.
Econometric Theory
also publishes interviews and articles on history; among the statisticians
interviewed are T. W. Anderson
and J.
Durbin.
·
Probability
and statistics now appear as topics in textbooks on the history of mathematics
and the history of disciplines that use probability and statistics. See for
example
V.J. Katz
(1993) A History of Mathematics,
M. Cowles
(2001) Statistics in Psychology: An Historical Perspective,
·
Articles
on the history of probability and statistics appear in several journals
including, Archive
for History of Exact Sciences Biometrika British Journal of the History of
Science Historia
Mathematica International Statistical Review Isis Journal
of the History of the Behavioral Sciences Statistical Science.
·
In
2005 a specialist online journal was
launched, Electronic
Journal for History of Probability and Statistics/Journal Electronique
d'Histoire des Probabilités et de la Statistique.
Online bibliographies
The JEHPS lists Publications in the History of Probability and Statistics. The current lists cover 2005-9.
Stigler’s History of Statistics has suggestions for further reading and an extensive bibliography. Hald’s History of Mathematical Statistics from 1750 to 1930 also has a very valuable bibliography.
There are several online bibliograpies. Two of the bibliographies were compiled in the mid-90s but are still useful—a brief one by Joyce, restricted to secondary sources, and an extensive one by Lee
Oscar Sheynin References
Giovanni Favero Storia della Probabilità e della Statistica
David
Joyce History
of Probability and Statistics
Peter M Lee The History of Statistics: A Select Bibliography
Online texts
Through the web many of
the important original texts are now easily accessible. The following open
access sites are very useful.
DML:
Digital Mathematics Library retrodigitized Mathematics Journals and Monographs
Life
and work of Statisticians
SAO/NASA ADS Astronomy
journals
Gallica particularly good for French literature
