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\noindent{\bf Harold JEFFREYS}\\
 b. 22 April 1891 - d. 18 March 1989
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\noindent{\bf Summary.} Harold
Jeffreys, a distinguished British geophysicist, advocated and justified the 
use of probability to describe one's beliefs about scientific ideas, and 
developed powerful methods for interpreting scientific data through 
probability.
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The career of Harold Jeffreys (1891-1989) is easily described. From
his local school in County Durham, he sent up to Cambridge, where
he stayed for the rest of his life.  His continuous 75 years as a
fellow of St. John's College is a record for any Oxbridge college.
He was Plumian Professor of Astronomy and Experimental Philosophy,
received numerous scientific awards and was knighted.

During most of his life, and certainly up until his retirement from
the Chair in 1958, he was best known for his important work in
geophysics and related fields.  His book, {\it The Earth: Its
Origin, History and Physical Constitution}, is a classic.  One of
the problems he studied was that of the transmission of earthquake
waves through the earth and, in particular, the interpretation of
seismological data.  As a result, he became interested in
statistical problems.  This interest was enhanced by the attention
paid in Cambridge of the 1920's to the philosophy of science.  This
combination of philosophy with scientific data culminated in the
publication in 1939 of his other great book, called simply {\it
Theory of Probability}.  The substantially revised third edition
appeared in 1961.  It is still in print and is considered by many
statisticians to be essential reading, not just for historical
reasons, but because of its modern manner of thought.  As Barnard
said ``There are a few [books] that are so far ahead of their time
that they are initially neglected and only reach their peak many
years after publication".  He was a poor oral communicator but his
writing is superb.  He stands, with literature's greatest, in the
effective use of the English language.

There are two major novelties in the {\it Theory}, as he liked to call
his book.  The first lies in the concept of probability: the second
in the development, from this concept, of practical procedures for
handling data.  He addressed the problem of how one's uncertainty
about quantities of scientific interest, like hypotheses or values
of constants, should be described.  In the first chapter he
demonstrated, on the basis of some simple ideas, in effect used as
axioms, that this could only be done through probability; so that
one could speak of the probability of a hypothesis being true.
Furthermore, statements of these uncertainties had to combine
according to the rules of probability.  One of these rules is
Bayes's theorem and because of its ubiquity, the subject, when
treated from this viewpoint, has become known as Bayesian
statistics.  The theory was the first modern book on Bayesian
statistics.  This attitude towards probability was quite different
from that of his near-contemporary, R.A. Fisher (q.v.), who was, in the
1930s, revolutionizing statistics.  Fisher used only the
probability of the data, given the hypothesis, whereas Jeffreys was
advocating and justifying the concept of the probability of the
hypothesis, given the data.  Fisher's ideas found general
acceptance and Jeffreys was initially treated as a maverick.

Views like Jeffreys's were also being developed by F.P. Ramsey
(also in Cambridge) and de Finetti in Italy.  They were later to be
expounded in the 1950s by L.J. Savage in the States.  Jeffreys went
further than these workers and developed operational techniques for
handling data.  Fisher was doing the same and it was possible to
compare the two procedures on a data set.  At the same time there
weemed to be good agreement but later work has revealed important
differences which are especially noticeable in the testing of
hypotheses.  Fisher's tests built on earlier ideas and used the
concept of a tail area.  If, on hypothesis $H$, a statistic $x$ has
probability density $p(x|H)$, the tail-area probability associated
with the observed value $x$ is $\int^{\infty}_{x}p(t|H)dt$,
sometimes called a $P$-value, or significance level.  Jeffreys
proceeded quite differently and in an original argument calculated
the probability of $H$, given $x$, $p(H|x)$.  This was based on a
prior probability of $H$, which he took to be $1/2$.  In important
numerical cases $p(H|x)$ can differ substantially from the
$P$-value.  An advantage of the broader view of probability is that
the resulting numbers, unlike $p$-values, are exactly those
required for decision-making.  Although Jeffreys, as the pure
scientist in his college, never considered decisions, his general
treatment has been found effective in management science and other
fields.

Jeffreys differed from de Finetti in regarding the numerical value
of a probability as being shared by all rational persons, whereas
de Finetti thought of it as subjective.  According to the latter
view, scientific objectivity only arises after substantial amounts
of data, relevant to a problem, have drawn differing subjective
views into agreement.  If Jeffreys was right, he had to have some
way of producing the rational probability.  The way he explored,
and which later workers have followed, is first to describe a
rational view of ignorance.  If a probability that represented
knowing nothing about a quantity, an extreme form of uncertainty,
could be developed, then any knowledge could update that
probability by Bayes's theorem, to produce rational opinions in the
light of that knowledge.  Ignorance played the role of an origin.
For example, a probability of $1/2$ seems to correspond to knowing
nothing about whether a hypothesis is true or not, being neutral
between the two possibilities.  A major advance in the later
editions of the Theory was the development of a probabilistic
description of ignorance using invariance concepts.  Jeffreys was
the first to recognise some inadequacies in his suggestions but
they have been very fruitful in leading later workers to develop
them into what nowadays are called `reference' or `default'
probabilities.

Jeffreys's views have influenced the philosophy of science, and are
in marked contrast to those of Karl Popper, who advocated the view
that a hypothesis could only be disproved, whereas probability
admitted values near one, effectively amounting to proof.  An
important illustration of the effect of this probabilistic thinking
on social and scientific questions is provided by contemporary
studies of global warming.  Is it taking place, due to industrial
and other pollutants, and, if it is, what will be its magnitude?
The probability school would calculate the probability of warming
using available data, and the conditional probability of its
magnitude, given that it exists.  Decisions based on these
probabilities can then be made rationally.  Generally, discourse on
important questions involving uncertainty should be conducted in
the language of probability.

Jeffreys worked largely on his own but his earlier, philosophical
ideas were developed with Dorothy Wrinch, who later became
well-known as an opponent of the ideas of Linus Pauling.  In 1940
he married Bertha Swirles.  They co-authored a splendid book on
{\it The Methods of Mathematical Physics}.  Jeffreys was a great
geophysicist who also created an original way of conducting the
scientific method.
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\begin{thebibliography}{3}
\bibitem{1}  His major statistical work is H. Jeffreys (1961).
{\it Theory of Probability}, 3rd Edition. Clarendon Press, Oxford.

\bibitem{2} 
H. Jeffreys \&amp; B Swirles (1956). {\it Methods of Mathematical
Physics}. Cambridge University Press, is popularly known as
`Jeffreys and Jeffreys'. 

\bibitem{3}  The issue of {\it Chance} magazine for
Spring 1991, {\bf 2, \#4}, is devoted to him and contains several
articles on his life and work, by Lady Jeffreys and others.  For
other references to Bayesian statistics, see under Thomas Bayes.
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\hfill{D.V. Lindley}

\end{thebibliography}

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