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\noindent{\bf Simon NEWCOMB}\\
b. 12 March 1835 - d. 11 July 1909
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\noindent{\bf Summary.} Noted Canadian born astronomer Simon Newcomb
contributed especially to the
treatment of outliers in statistics and to the application of probability
theory to data.
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Much of the early development in statistics originated in problems oo
astronomy. The development of least squares by Gauss (q.v.)
and Laplace (q.v.) was because
of its importance in astronomy. Problems of outliers, and attendant rejection
rules, often were introduced in astronomy. The theory of weighted least
squares also originated in attempts to assess variability of different
data sets measuring the same quantity (Stigler, 1973). One of the leading
astronomers in the United States during the late 19th century was
Simon Newcomb, whose contributions to probability and statistics must not
be overlooked.
Simon Newcomb was born in northern Nova Scotia, Canada, in 1835. His father
was a country school teacher, and the family moved about a lot. His schooling
came mainly from reading books that his father obtained for him. At age 16
he needed to start work, and after a stint as an apprentice to a dishonest
quack of a medical doctor, he became a school teacher and tutor. In 1857 he
was employed as a computer at the American Ephemeris and Nautical Almanac
in Cambridge, Massachusetts.
The Almanac office duties were limited, and Newcomb managed to combine
his work with studies towards a B. Sc. under Benjamin Pierce at Harvard,
which degree he obtained in 1858. In 1861 he was appointed professor of
mathematics at the Naval Observatory, and in 1877 he also became
Superintendent of the Nautical Almanac. He died in 1909, and left behind
an impressive legacy of publications (Archibald, 1924 lists 541 published
works).
While Newcomb's main contributions were astronomical (he made detailed
calculations of the paths of moon and the planets), from a statistical point
of view his main contributions were in applying probability theory to
data, and in developing what we now call robust statistical methods.
A sequence of Notes on the Theory of Probabilities (Newcomb, 1859-61) were
published in a short-lived mathematical problems journal called {\it Mathematics
Monthly}, to which Newcomb was a frequent contributor. These Notes constitute a
brief textbook in elementary probability theory, which looks quite up-to-date
even today. Among the most interesting examples he works out are an application
of the Poisson process to assess whether or not the Pleiades could result
from a random distribution of stars. In fact, he determines the ``probability
that, if the stars were scattered at random over the heavens, any small sphere
selected at random would contain $s$ stars." For a region of size 1 squared
degree, and assuming that there are about 1500 stars of fifth and higher
magnitude, Newcomb finds the probability of having six stars in this region
about $1.28 \times 10^{-7}$. While he does not explicitly describe a Poisson process
(neither does Clausius, 1858, who arguably is the first scientist to use
this process), his calculation makes it clear that ``scattered at random"
means independently distributed over disjoint sets.
Another interesting application of probability theory to data was Newcomb's
discovery of the logarithmic distribution (Newcomb, 1881) as the distribution
of leading digits in haphazardly chosen numbers.
Perhaps the most important contribution of Newcomb in the statistical area
was his approach to dealing with outliers in astronomical data. From looking
at substantial amounts of data it was clear to him that a normal distribution
of errors was inadequate, since the observed tails of the distribution often
were fatter than what the normal distribution would require. For example, in
looking at a collection of 684 observations of transits of Mercury
(Newcomb, 1882) the non-normality could not be explained even by removing
some extreme observation. However, it could be the result of
combining data with different precision, and the idea of a mixture of
normal distributions would therefore seem close at hand. Thus, the contaminated
normal distribution was invented.
In a later paper Newcomb (1886) criticized outlier rejection criteria, and
developed a new estimation procedure which weighted ``more discordant"
observations less heavily. The basic idea is to fit a mixture of mean zero
normals to the residuals from the sample mean, and compute a posterior
mean with respect to a uniform prior for the normal mixture model.
In fact, in later papers (cf. Stigler, 1973) Newcomb criticized outlier
rejection techniques for being discontinuous in the data, in essence
developing Tukey's sensitivity function, and proposed Huber's M-estimator
as a simple robust estimator.
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\begin{thebibliography}{3}
\bibitem{1}
Archibald, R. C. (1924). Simon Newcomb 1835-1909. Bibliography of his life and
work. {\it Memoirs of the National Academy of Sciences}, {\bf 17}, 19--69.
\bibitem{2}
Campbell, W. W. (1924). Biographical Memoir Simon Newcomb 1835-1909.
{\it Memoirs of the National Academy of Sciences}, {\bf 17}, 1--18.
\bibitem{3}
Clausius, R. (1858). \"{U}ber die mittlere L\"{a}nge der Wege, welche bei
Molekularbewegung gasf\"{o}rmigen K\"{o}rper von den einzelnen
Molec\"{u}len zur\"{u}ck gelegt werden, nebst einigen anderen Bemerkungen
\"{u}ber die mechanishcen W\"{a}rmetheorie. {\it Annalen der Physik} {\bf 105}, 239--258.
\bibitem{4}
Newcomb, S. (1859-61). Notes on the Theory of Probabilities. {\it
Mathematics Monthly}
{\bf 1}, 136--139, 233--235, 331--355, 349--350; {\bf 2}, 134--140, 272--275;
{\bf 3}, 68, 119--125, 341--349.
\bibitem{5}
Newcomb, S. (1881). Note on the frequency of use of different digits in
natural numbers. {\it American Journal of Mathematics}, {\bf 4}, 39--40.
\bibitem{6}
Newcomb, S. (1882). Discussion and Results of Observations on Transits of
Mercury from 1677 to 1881. {\it Astr. Papers}, {\bf 1}, 363--487. Published by
the U.S. Nautical Almanac Office.
\bibitem{7}
Newcomb, S. (1886). A generalized theory of the combination of observations so
as to obtain the best result. {\it American Journal of Mathematics}, {\bf 8}, 343--366.
\bibitem{8}
Stigler, S. M. (1973). Simon Newcomb, Percy Daniell, and the History of Robust
Estimation 1885-1920. {\it Journal of the American Statistical Association},
{\bf 68}, 872--879.
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\hfill{Peter Guttorp}
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