# BIOGRAPHICAL MEMOIRS

**Edmund Alfred Cornish 1909-1973**

This memoir was originally published in *Records of the Australian
Academy of Science*, vol.2, no.4, 1973.

Edmund Alfred Cornish was born in Perth on 7 January 1909. He was the son of William Alfred Cornish and Ruby Ada (née Ovey), and had a younger brother and sister. His father was keen on his education and trained his memory from a very early age. In fact by the age of four he could recite Oliver Goldsmith's 'The Deserted Village', and all the towns on the river Volga. After primary schooling in Perth he went to Wesley College, Melbourne, which he left without matriculating but where he probably acquired his lifelong interest in cricket. After a short interval he returned to Wesley where he obtained his matriculation and began his studies in the Faculty of Agriculture in the University of Melbourne. Here he graduated in 1931 with first class honours in Agricultural Biochemistry and in Agricultural Engineering and Surveying, and won the James Cuming Prize in Agricultural Chemistry and Agricultural Biochemistry. He was then appointed Agrostologist at the Waite Agricultural Research Institute. Here he was confronted with the statistical problems arising in agriculture and began to study the subject seriously, to such good effect that by the end of 1936 he had already published four papers. In the first of these (written with Professor H.C. Trumble) he began the study of the relationship between meteorological variables and agricultural yields which was to occupy much of his research time in later years. Moreover in the fourth of these papers he put forward the conclusions that there was a 23 year period in Adelaide rainfall. In an immediately following paper in the same journal F.J.W. Whipple pointed out that this oscillation was in phase with twice the period of the sunspot cycle, thus confirming earlier claims by Abbott, Douglass and others that there exists a 23-year cycle in solar radiation. This 23-year cycle might be the result of the fact that the sunspot cycle is really twice its apparent length, the magnetic polarity reversing in each cycle. The existence of a 23-year cycle in weather seems to have been confirmed by later work but the importance of Cornish's contribution was to observe that the variation occurs not in the total annual rainfall but in the time of arrival of the rainy season. However by basing his observations on 10-year moving averages, which remove most of the contribution to the spectrum of any 11-year oscillation, he deprived himself of the opportunity of testing whether the 11-year cycle itself had any effect. At this time the implications of spectral analysis in studying time series were not widely appreciated and further analysis of his derived series would be of great interest.

During this time Cornish was pursuing spare time studies in mathematics
at the University of Adelaide where he was given much encouragement
by Professor J.R. Wilton,
a distinguished Australian mathematician widely known for his
researches in analytical number theory. At first these studies
aroused the disapproval of his superiors who could not see why
an agrostologist should study mathematics. This attitude soon
changed when it was realised how much help he could give his colleagues.
In 1937 Cornish, who had been in correspondence with Sir Ronald Fisher,
took leave of absence at his own expense to study at University
College, London, with Fisher. One outcome of this experience was
the much quoted paper, 'Moments and cumulants in the specification
of distributions' (with R.A.Fisher), *Inst. Intern. de Stat.
Rev.*, 5, 307-322, 1937, on the use of moments and cumulants
to provide approximations to distributions. This led to further
work by Cornish and others which is still continuing. In 1940
he obtained his MSc, and in 1951 a DSc from the University
of Adelaide.

On his return from England in 1938 Cornish was appointed Statistician to the Waite Institute. In 1941 the Council for Scientific and Industrial Research (now the CSIRO) had the vision to create a section of Mathematical Statistics (known at this time as the 'Section of Biometrics'), and appointed Cornish as its head. This was sited in 1944 in the grounds of the University of Adelaide, to the profit of both institutions. In fact the CSIR had had up to this time a very small biometrical section for a number of years, which for most of this time consisted of Miss F.E. Allan (later Mrs J. Calvert) and Miss M. Barnard (later Mrs S.A. Prentice) both of whom had done notable early work on theoretical statistics. Here he organised a group which included E.J. Williams, G.A. McIntyre and Helen Turner, all of whom later achieved fame as statisticians. The value of this Section to Australian science quickly became apparent and in 1954 it became a CSIRO Division with Cornish as its Chief. Besides doing research in varied aspects of mathematical and applied statistics, many of its scientific officers were attached to other Divisions as consultants.

Meanwhile the University of Adelaide had become aware of the need for the teaching of mathematical statistics and appointed Cornish as a part-time lecturer, a post which he held until 1960 when he was appointed Foundation Professor of Mathematical Statistics for a five year term. He held this post simultaneously with his post as Chief of the Division. The appointment was made for the purpose of getting a department established and at the end of the five year term he relinquished it to A.T. James, a former student and officer of his Division who had achieved fame for his fundamental work in multivariate analysis and who at that time was Professor of Statistics at Yale. Meanwhile Cornish continued as Chief of the Division and was planning to retire when he died suddenly on 31st January 1973. At this time the Division had about 50 scientific staff.

Cornish was married in 1935 to Marion Jessie Davis and had two daughters and two sons. After his wife's death he married Gene May Goodale in 1965.

After Cornish's return from England most of his published papers in the next ten years were on methods of analysis in experimental designs. However in 1949 and 1950 he returned to statistical meteorology in two long papers on the effect of rainfall in South Australia on wheat yields. These were the result of a very large scale investigation into the subject, and led him to restudy the secular variation in Adelaide rainfall.

The remaining four papers on climatology were not concerned with agricultural yields but with climatology itself. In a paper written with G.G. Coote, he found the regression of monthly values of rainfall in South Australia at 97 rainfall stations on their altitude, and longitude and latitude, a large calculation but one which enables more accurate isohyets to be obtained, since the residual variance was small. In a paper with N.S. Stenhouse, and in one with G.W. Hill and Marilyn J. Evans, he calculated the correlations of rainfall between different stations using in the first case 25 stations and monthly rainfall, and in the second 55 stations and six-day periods throughout the year. The size of this work can be seen from the fact that the second of these papers involved the calculation of 90,585 correlation coefficients. Having obtained the correlations these were regressed, after transformation, on the distance and orientation of each pair of stations. These results were then related to the synoptic meteorology of the area.

In his last paper on climatology, written with Marilyn J. Evans, he considered temperatures at a single station in Adelaide and six-day averages of daily maximum, minimum and mean temperatures. To these he applied similar techniques to those used for rainfall. Further investigations on South Australian rainfall and wheat yields were nearly complete at the time of his death and are in course of being prepared for publication. In summary, it seems likely that never before has such large scale and penetrating statistical analyses been made on the climatological data of a single area.

In 1954 he started on a new line of research, that of multivariate
analysis, which was to become the other of his two major contributions
to statistics. It is widely believed that mathematicians do their
best original work before they are thirty but this is often false.
Cornish was now forty-five and his work had so far been in the
application of known statistical theory, but he now began to publish
in one of the most technical parts of mathematical statistics,
and was to continue working in this field for the rest of his
life. He began by inventing and discussing in detail a multivariate
t-distribution. This is quite a different type of generalisation
from Hotelling's well known T^{2}-distribution which is a natural
generalisation of Student's t-distribution to samples from a multivariate
normal distribution. Cornish's distribution, however, is the joint
distribution of the deviations of the sample values from a univariate
normal distribution, divided by the common estimate of their standard
deviation. In two papers, he discusses the properties of this
distribution in great detail.

As a student of R.A. Fisher, Cornish was a firm believer in fiducial inference, a subject of wide controversy amongst statisticians. Using this approach he studied the testing of compound hypotheses, and in a series of papers he applied his generalised t-test to obtain the fiducial distributions of the means in multivariate situations. If the fiducial argument is accepted, he obtained in this way tests for the means of multivariate normal distributions which are uniformly more powerful than Hotelling's test. Even to those who disagree with Fisher's approach these results are of very considerable interest and involve some elaborate mathematical analysis. In particular the discussion which follows is worth study by every statistician.

Whilst carrying out research he was continuously under the strain of administering and leading a steadily growing Division, a particularly arduous task requiring much travelling, as the members of the Division were widely scattered over Australia. Although a rather reserved man, his combination of personal sensitivity and scientific imagination enabled him to pick a long series of recruits who not only made a name for the Division abroad by their own research but also contributed in a very large way to the research of other Divisions. He also spent a great deal of time and energy in helping them in their personal affairs.

When Cornish began in the CSIRO all statistical computations were made on hand-operated machines. With the advent of electronic computers not only was this task greatly eased but a whole host of new problems arose for it was now possible to carry out traditional methods of statistical analysis at a very high speed, and consequently to do problems which were previously too large. Moreover, it was now also possible to answer many statistical problems by simulation. Cornish was one of the first to realise this. He not only convinced the CSIRO that it should begin to use computers more widely but ultimately that they should set up a Division of Computing Research which was founded in 1963. Thus his vision and insight led to the founding not of one but of two of the Divisions of CSIRO.

When R.A. Fisher retired from the Balfour Chair of Genetics at Cambridge he remained there until 1959 when he took the opportunity of coming to Australia as a Senior Research Fellow in Cornish's Division in Adelaide. Here, more or less continuously, he remained until his death in 1962, during this time contributing greatly to the benefit of the Division. Subsequently his collected papers were prepared for publication by Cornish and Professor J.H. Bennett and three volumes of these have already appeared.

In 1951 Cornish received the Australian Medal of Agricultural Science awarded by the Australian Institute of Agricultural Science 'for distinguished services to agriculture', and the same Institute elected him a Fellow in 1958. He was elected a member of the International Statistical Institute in 1951, an Honorary Fellow of the Royal Statistical Society in 1968, and a Fellow of the Australian Academy of Science in 1954. In 1956-57 he was President of the (international) Biometric Society and on its Council for 1970-72 and 1973-75. He was an Associate Editor of Biometrics 1951-64 and foundation President of the Australasian Region for 1948-50. He attended a number of international conferences and in 1969 delivered the third R.A. Fisher Memorial Lecture in the University of London, which was a survey of further work on the Fisher-Cornish expansion by himself and his colleagues. Unfortunately this has not been published.

By his death Australia has lost a distinguished statistician whose services to his country were greater than generally recognised.