# Patrick Alfred Pierce Moran

### Quick Info

Kings Cross, Sydney, New South Wales, Australia

Canberra, Australian Capital Territory, Australia

**Patrick Moran**was an Australian statistician who worked in probability theory and its application to population and evolutionary genetics.

### Biography

**Patrick Moran**was the son of Herbert Michael Moran (1885-1945) and Eva Mann (1887-1977). Herbert Moran, the son of Michael Moran (1856-1951), was a surgeon in Sydney who specialised in treating cancer patients. Michael Moran, Patrick Moran's paternal grandfather, was born in Ireland and arrived in Australia in 1877 becoming a successful baker in Sydney. Eva Mann's family had come to Australia some years before Herbert Moran's family. All her ancestors were in Australia by 1830. Except for Patrick's father, all other members of the families were without a formal education. Herbert and Eva Moran had six children, Patrick being the first born, but all the other five died shortly after birth.

Patrick Moran was clearly strongly influenced by his father although he wrote later in life in autobiographical notes (see [18] or [19]):-

I did not understand him at all ... yet I appreciated him.His father had an extensive library with many books on the history of medicine and on science in general. Peter Hall writes [15]:-

As a small boy he was very interested in mechanical devices, but did not show a particular aptitude for mathematics. He was later to write, "Arithmetic I could not do and never got my sums right all through schooldays (and later in the Ministry of Supply!)."An event which left him with a permanent husky voice happened in his childhood when [18]:-

... he suffered an attack of appendicitis late one night after going out with his parents for a meal. His father panicked and phoned for a distinguished surgeon colleague who operated around midnight, too soon after the meal. Pat vomited on the operating table and the surgeon had to do a tracheotomy to let him breathe, cutting his vocal cords in the process.In 1928 Moran was sent to St Ignatius College, Riverview, an old Sydney school, for a few terms but then was educated at home for over a year. Some of the breaks in Moran's education were due to his father travelling to Europe to learn about the latest developments in cancer treatment. Around 1930 he read W H Turnbull's small book

*The Great Mathematicians*and this made him 'determined to be a mathematician' despite his lack of arithmetical skills. In 1930 he entered St Stanislaus College in Bathurst, a town in rural New South Wales. Pat's memories of life at this school were mostly unhappy but he had a 'lasting respect for the headmaster, Father E Gallagher' who, he wrote later in life, 'encouraged me to think'. He matriculated from St Stanislaus in 1933, despite having missed six months schooling in 1932 when he was with his father in Europe.

Moran entered Sydney University in 1934, before reaching his 17th birthday, aiming to study various sciences but to specialise in mathematics. He studied chemistry for one year, zoology for two years and mathematics and physics for three years. We are fortunate to have details of some of the mathematics courses he took. In pure mathematics these included a course by Richard Jenkins Lyons on analytical geometry and two courses by Thomas Gerald Room, one on algebra and one on higher plane curves. In applied mathematics the courses included two by H H Thorne, one on statistics and one on the kinetic theory of bases, and a course by E M Wellish on wave mechanics. He graduated in 1937 with a first class degree in mathematics. One sadness of the three years he spent as an undergraduate was that his parents were divorced in 1935.

After graduating, Moran continued studying aiming at the mathematical tripos at the University of Cambridge. He wanted to undertake research in mathematics but Horatio Scott Carslaw, who retired from the Chair of Mathematics at Sydney in February 1935, told him to choose a different subject since Carslaw believed he would not succeed as a mathematician. After this Moran's father tried to persuade him to study medicine but Moran was keen to stick with mathematics. He travelled to England with his mother in September 1937 with the promise of financial support from his father. He entered St John's College and was a Wrangler in Part II of the tripos in 1938. He was 28th out of 33 Wranglers and continued to Part III. He attended a variety of courses in 1938: J A Todd on differential geometry, M H A Newman on analysis, A E Ingham on algebra, H Heilbronn on the theory of numbers, S Goldstein on electricity and hydrodynamics, E Cunningham on statics and dynamics, J C Burkill on theory of real functions and W W Rogosinski on Fourier series. In 1939 he took courses: M H A Newman on topology, A S Besicovitch on integration, F Smithies on integral equations, J C Burkill on the theory of real functions, W W Rogosinski on Fourier series, and G U Yule on statistics. He also attended lectures by G H Hardy in 1938-1939. Moran passed the examinations for Part III in June 1939 but his supervisor, Ebenezer Cunningham, told him "that [he] had no real mathematical ability and that he should do something else, e.g. medicine." Despite receiving the same advice from two independent experts, Moran was still determined to continue his study of mathematics. Robert Rankin [19]:-

... recalls that Pat had lodging near Darwin College where Besicovitch lived and that he used to take Mrs Besicovitch occasionally to the cinema for which Besicovitch always thanked him when next they met. He also recalls Pat's troubles with arithmetic through an incident of considerable exasperation to Pat when he worked something out three times and obtained a different answer on each occasion. Pat himself was to write, "Arithmetic I could not do."Moran decided to wait a year before beginning research and aimed at studying logic in the Moral Sciences tripos. When World War II began in September 1939, Moran's plans had to change and he was appointed as an experimental officer in the Ministry of Supply, working on rockets at the Projectile Development Establishment. At this stage he met D G Kendall who remembered their first meeting well [19]:-

I recall very clearly the day on which I first met Pat Moran. It was 1 February 1940; we had each been summoned for interview, and the object of this (though we did not know it at the time) was to build up a team of mathematicians to work on rocket weapons under W. R. J. (later Sir William) Cook and Louis Rosenhead. I arrived a little late, and the waiting room contained a group of people nearly all of whom were complete strangers to me, though they seemed to know one another well. One was Pat, and he beamed a terrific smile in my direction when he saw my embarrassment. We instantly became great friends.Moran recalled [15]:-

... working in a room with Maurice Bartlett, and looking through Fisher's 'Statistical Methods for Research Workers'. It seemed then very clear to me that I would never understand statistics.This work bored him so he moved to External Ballistics Laboratory in Cambridge. This he found even worse as he was required to only make routine calculations for problems he was not allowed to know about. Leaving this job, in 1942 he joined the Australian Scientific Liaison Office in London. Here his work involved both applied physics and operational research. He took a course on radar and visited operational research sections of Fighter Command, Coastal Command, Bomber Command and several other units. He wrote up reports, over 120 in all, and began research, in particular on measuring the mean projected area of a shell fragment, a topic proposed by D G Kendall. Realising that a deeper knowledge of statistics would benefit him, he read the first volume of M G Kendall's

*Advanced Theory of Statistics*which inspired him. Joining the Royal Statistical Society, he spent his lunch times in their library and got to know M G Kendall.

While studying mathematics at Cambridge it had been Besicovitch who had the most influence and, during the war years, Moran undertook research on Hausdorff measure publishing several papers on the topic, including

*The measure of plane sets*(1943),

*Measuring the surface area of a convex body*(1944), and

*The measure of product and cylinder sets*(1945) which was a joint publication with Besicovitch. Leaving the Australian Scientific Liaison Office in June 1945, he was awarded a Baylis Research Scholarship to undertake research at St John's College, Cambridge. He had hoped that Besicovitch would supervise his research but he was rather saddened to find that Besicovitch did not want to do so and instead suggested that he work with Frank Smithies.

Choosing the right research problem for a research student is not the easiest thing to do since one has always to find a problem which will lead to results even if the original problem proves too hard. Smithies did not make a good choice in what he proposed to Moran since the problem proved far too hard; indeed it has still not been solved. Moran made no progress but for relaxation worked on statistical problems suggested to him by Maurice Kendall and John Wishart. He also attended lectures by Maurice Bartlett on the relation between Rimkowski theory of mixed area and analysis of variance and Edward Bullard's lectures on economics. After a year working on the problem posed by Smithies, in 1946 Moran gave up his scholarship and was appointed as a Senior Research Officer at the Institute of Statistics at the University of Oxford. This had, at least in part, been the route that he took so that he was in a sound enough financial state to marry.

Moran had met Jean Mavis Frame (born 1918) in 1945 and they were married on 14 September 1946 in Reading; they had three children, Everill Frances Louise Moran (born 1947), Michael Patrick Allan Moran (born 1950) and Hugh Frederick Moran (born 1953). For most of their lives in Australia from the 1950s onwards they lived at 17 Tennyson Crescent, Forrest in Canberra.

Some of the first papers he published on statistics were

*Random associations on a lattice*(1947),

*The random division of an interval*(1947),

*Some theorems on time series*(1947),

*On the method of paired comparisons*(1947), and

*Rank correlation and permutation distributions*(1948).

Working at the Institute of Statistics at the University of Oxford, Moran was attached to Balliol College and later lectured at Trinity College. Perhaps the most significant thing, at least as far as his future career was concerned, about this position in the Institute of Statistics was that it was housed beside the Bureau of Animal Population and the Edward Gray Institute of Ornithology. His contacts with these two led to a lifelong interest in animal populations and many of his later publications arose through this interest. In 1951 Moran was appointed as a University Lecturer at Oxford but he returned to Australia at the beginning of 1952 when he was appointed as foundation professor of statistics at the Australian National University in Canberra. This was a slightly unusual appointment since the Statistics Department had been set up in the Research School of Social Sciences but Moran had no interest in the Social Sciences [19]:-

Initially Pat had no staff and no students, but the library facilities were good from the outset. He was 34 years of age at the time and comparatively inexperienced, but with a combination of good luck and good judgement the department which he founded prospered. Although it typically had only three or four academic staff and never had more than seven during the thirty years of his tenure, it played a unique role in the training and development of several generations of Australian statisticians.Moran's contributions in many areas were very influential. One of the first areas he worked on after taking up the statistics chair in Canberra led first to the paper

*A probability theory of dams and storage systems*and, after a series of others on the topic, the book

*The Theory of Storage*(1959). Before this book appeared his first paper on genetics appeared with

*Random processes in genetics*(1958). Again he wrote an important book in this area with

*The Statistical Processes of Evolutionary Theory*(1962). As an example of his work on animal populations, let us mention the paper

*Some remarks on animal population dynamics*(1960) published in

*Biometrics*. In 1963 he published the book

*Geometrical Probability*written in collaboration with Maurice Kendall. The fourth of Moran's books was

*An Introduction to Probability Theory*(1967). He writes in the Preface:-

Holding as I do, the view that however important abstractions and generalisations are, no mathematical science can remain vigorous unless it draws some of its inspiration from the natural sciences, an attempt has been made to illustrate the subject by some of the many attractive problems in what has now come to be known as 'applied probability theory'.In a review of this book in the

*Journal*of the American Statistical Association, the reviewer writes:-

This classic text and reference introduces probability theory for both advanced undergraduate students of statistics and scientists in related fields, drawing on real applications in the physical and biological sciences. The book makes probability exciting.For some extracts from reviews of Moran's four books, see THIS LINK.

Moran kept up contacts with other statisticians both through visits abroad and having visitors come to Canberra. For example he spent a month visiting Jerzy Neyman at the University of California at Berkeley in each of the years 1965, 1970 and 1971. He spent a year at the University of Oxford in both 1955-56 and in 1960. On the 1960 visit he returned to Australia on the ship Southern Cross, leaving Southampton on 6 December and arriving in Sydney. In 1966 he spent study leave in the USSR and made a trip to China in 1979-80.

C C Heyde describes Moran's personality in [18]:-

For the most part, people saw Pat as unaffected, quiet, friendly and courteous. There was, however, a darker side to his personality and he suffered considerably from depression. His religious beliefs were deeply held and when he realized he had made a mistake he would typically try to make amends.In 1982 he reached the age of 65 and retired from his chair. Made an honorary Visiting Fellow in the Social Psychiatry Research Unit he published a number of papers

*British Journal of Psychiatry*. His interest in mental disorders almost certainly arose because of the depression from which he suffered. He had little contact, however, with the department which he had led for thirty years which saddened his colleagues who greatly appreciated his deep knowledge and insight. A stroke in July 1987 left him with paralysis down his left side but with determination on both his part and that of his wife, he slowly recovered. A heart attack in September 1988 ended his life. He was buried in Gungahlin Cemetery, Mitchell, Canberra.

Moran was honoured for his outstanding research by election to the Australian Academy of Science in 1962 and also to the Royal Society of London in 1975. The Australian Academy of Science awarded him their Lyle Medal in 1963 and the Statistical Society of Australia awarded him their Pitman Medal in 1982. He was made an Honorary Life Fellow of the Royal Statistical Society in 1970 and an Honorary Life Member of the Statistical Society of Australia in 1978. He served as President of the Statistical Society of Australia (1963-64), President of the Australian Mathematical Society (1976-78), and Vice-President of the International Statistical Institute (1975-77). He was also honoured after his death by having the Australian Academy of Science beginning the award of the Moran Medal in 1990. The Academy's webpage gives the following information about the Medal:-

The Moran Medal recognises the contributions to science of the late P A P Moran, FAA. Its purpose is to recognise outstanding research by scientists under 40 years at the closing date, except in the case of significant interruptions to a research career, in one or more of the fields of applied probability, biometrics, mathematical genetics, psychometrics and statistics. The award is normally made every two years.For winners of the Moran Medal, see THIS LINK.

### References (show)

- D E Barton, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Journal of the Royal Statistical Society. Series A (General)***128**(4) (1965), 596-597. - D E Barton, Review: The Statistical Processes of Evolutionary Theory, by P A P Moran,
*Biometrika***53**(1/2) (1966), 299-300. - D E Barton, Review: The Theory of Storage,
*Biometrika***48**(1/2) (1961), 231. - H H Campaigne, Review: The Theory of Storage, by P A P Moran,
*Mathematics of Computation***14**(72) (1960), 393-394. - R M Cormack, Review: The Statistical Processes of Evolutionary Theory, by P A P Moran,
*Science Progress (1933-)***50**(200) (1962), 679-680. - F N David, Review: The Theory of Storage, by P A P Moran,
*Science Progress (1933-)***48**(192) (1960), 758-759. - F N David, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Biometrika***51**(3/4) (1964), 532. - F Downton, Review: The Theory of Storage, by P A P Moran,
*The Mathematical Gazette***45**(354) (1961), 368. - F G Foster, Review: The Theory of Storage, by P A P Moran,
*Journal of the Royal Statistical Society. Series A (General)***123**(4) (1960), 485-486. - D A Freedman, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Econometrica***31**(4) (1963), 780-781. - J K Friend, Review: The Theory of Storage, by P A P Moran,
*Operational Research***13**(1) (1962), 104-106. - B Fristedt, Review: An Introduction to Probability Theory (1967), by P A P Moran,
*Journal of the American Statistical Association***81**(393) (1986), 264-265. - J Gani, Patrick Alfred Pierce Moran, 1917-1988,
*Bull. Inst. Math. Statist.***17**(1988), 449. - J Gani and E J Hannan (eds.),
*Essays in Statistical Science*(1982) (J. Appl. Prob., Special Volume 19A). - P G Hall, Obituary: Patrick Alfred Pierce Moran, 1917-1988,
*Biometrics***45**(2) (1989), 687-692. - E J Hannan, Some memories of Pat Moran,
*J. Appl. Prob.***6**(1989), 215-218. - C C Heyde, Patrick Alfred Pierce Moran. Died 19 September 1988, Elected to Fellowship 1962,
*Australian Academy of Science Year Book*(1990-91), 81. - C C Heyde, Patrick Alfred Pierce Moran 1917-1988,
*Historical Records of Australian Science***9**(1) (1991). - C C Heyde, Patrick Alfred Pierce Moran 1917-1988,
*Biographical Memoirs of Fellows of the Royal Society of London***37**(1991), 365-379. - N L Johnson, Review: The Theory of Storage, by P A P Moran,
*Journal of the Institute of Actuaries (1886-1994)***86**(1) (1960), 104-105. - H Kaufman, Review: The Theory of Storage,
*Amer. Math. Monthly***68**(1) (1961), 74. - J M Hammersley, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*The Mathematical Gazette***48**(365) (1964), 328-330. - A Huitso, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Journal of the Royal Statistical Society. Series D (The Statistician)***14**(1) (1964), 77-78. - M Kimura, Review: The Statistical Processes of Evolutionary Theory, by P A P Moran,
*The Quarterly Review of Biology***39**(1) (1964), 86. - J F C Kingman, Review: An Introduction to Probability Theory (1967), by P A P Moran,
*Journal of the Royal Statistical Society. Series A (General)***132**(1) (1969), 106. - P M Morse, Review: The Theory of Storage,
*Operations Research***9**(6) (1961), 919. - A Rényi, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Revue de l'Institut International de Statistique / Review of the International Statistical Institute***31**(3) (1963), 449-450. - H Scarf, Review: The Theory of Storage, by P A P Moran,
*Journal of the American Statistical Association***56**(294) (1961), 411. - J Sethuraman, Review: Geometrical Probability, by M G Kendall and P A P Moran,
*Sankhya: The Indian Journal of Statistics, Series A (1961-2002)***30**(1) (1968), 116-117. - C A B Smith, Obituary: Pat Moran, 1917-1988,
*J. Roy. Statist. Soc. A***152**(1989), 419. - P L Workman, Review: The Statistical Processes of Evolutionary Theory, by P A P Moran,
*Journal of the American Statistical Association***58**(302) (1963), 575. - S Wright, Review: The Statistical Processes of Evolutionary Theory, by P A P Moran,
*American Scientist***50**(4) (1962), 460A.

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Written by J J O'Connor and E F Robertson

Last Update September 2018

Last Update September 2018