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BIOGRAPHICAL MEMOIRS

Patrick Alfred Pierce Moran 1917-1988

Introduction University in Sydney and Cambridge, 1934-1939 Civil service, 1940-1945 Oxford, 1946-1951 Professor at ANU, 1952-1982 Emeritus years, 1983-1988 Personal Additional personal biographical notes Some notes on Pat Moran's contribution to mathematical statistics and biomathematics References Acknowledgements

By C.C. Heyde

This memoir was originally published in  Historical Records of Australian Science, vol.9, no.1, 1991. It was also published in  Biographical Memoirs of Fellows of the Royal Society of London, 1991.

Patrick Alfred Pierce Moran was born in Kings Cross, Sydney on 14 July 1917. He was the first of six children of Herbert Michael Moran (b. 1885 in Sydney, d. 1945 in Cambridge UK) and his wife Eva (née Mann) (b. 1887 in Sydney, d. 1977 in Sydney). The other siblings died at or shortly after birth. H.M. Moran was a Sydney surgeon who specialized also in the radium treatment of cancer. Pat's paternal grandfather, Michael Moran (1856-1951), was the son of a small tenant farmer in Ireland: he came to Australia in 1877 and was a successful baker in Sydney. His paternal grandmother, who died young, was born in Dungog, NSW, in 1860. Both her parents were Irish. His mother's ancestors were all in Australia by 1830. Her father's family were English Protestants and her mother's mostly Irish Catholics. None of Pat Moran's forebears, other than his father had any connection with science or indeed any formal education.

Pat Moran was significantly influenced by his father Herbert, although he wrote in autobiographical notes that 'I did not understand him at all...yet I appreciated him'. Herbert Moran had a considerable interest in science and he collected a large library, including many books on the history of medicine and also on science. In addition he subscribed to  Nature  and at one stage he employed J.M. Somerville, then a research student in Sydney and later a professor at Armidale, to tutor him in physics, especially radioactivity. Pat absorbed the atmosphere and was fascinated by many of the books. In particular, at about age 13 he read W.H. Turnbull's small book on  Great Mathematicians  and 'determined to be a mathematician'.

Herbert Moran travelled frequently to Europe, especially to keep in touch with developments in cancer treatment, and Pat Moran's education was very interrupted. He went to St Ignatius College, Riverview, for several terms in 1928 and then was tutored at home for a year or so. In 1930 he was sent to St Stanislaus College, Bathurst, and despite some six months in Europe in 1932 he matriculated from this school at the end of 1933, having finished the five-year course in three and a half years. Pat was 'acutely unhappy' at the school but he did develop a 'lasting respect for the headmaster, Father E. Gallagher' who, he reported, 'encouraged me to think'

University in Sydney and Cambridge, 1934-1939

Pat entered the University of Sydney at age 16 in 1934 to study Science as one of a group of whom four were subsequently to be elected FRS, namely J. Cornforth, R. Nijholm, D. Waterhouse and Pat, while M. Day became FAA and V. Burgmann became Chief Executive Officer of CSIRO. Cornforth was awarded the Nobel Prize for Chemistry in 1975.

At university, Pat studied chemistry for one year, zoology for two years and mathematics and physics for three years. He obtained a High Distinction in mathematics in each year and graduated in 1937 with First Class Honours in that subject. The breadth of his training was important, however, and he described the two years of zoology as 'of enormous value...later'

After completing his examination, Pat began to study for Cambridge. His father did not want him to continue with mathematics in view of a letter from the Sydney professor of mathematics, H.S. Carslaw, advising that Pat 'should choose some other career as he would not succeed as a mathematician'. Indeed, his father wanted Pat to do medicine.

Pat was, nevertheless, financially supported by his father and travelled to Cambridge in September 1937 together with his mother, who had separated from his father in 1935. He entered St John's College together with the then Barker Scholar from Sydney, Frederick Chong, subsequently professor of mathematics at Auckland and Macquarie Universities. They were both Wranglers in the Tripos (Part II) in 1938, Pat being 'unofficially about 28th out of a class with 33 Wranglers'.

Pat continued with Part III of the Tripos, taking lectures from A.S. Besicovitch, W.W. Rogosinski, G.H. Hardy, M.H.A. Newman, F. Smithies, J.A. Todd and S. Goldstein and he passed the examinations in June 1939. He was 'very disappointed' at his failure to gain a Distinction and his supervisor, Mr E. Cunningham, told him 'that [he] had no real mathematical ability (he agreed with Carslaw!) and that he should do something else, e.g. medicine'. Pat remained unconvinced, however, but realized that he was still too immature to do research. He decided to do Part II of the Moral Sciences Tripos (in Logic) but the outbreak of war in September 1939 intervened.

At this stage Pat had little background in statistics. He had attended G.U. Yule's course on vital statistics at Cambridge in 1939 but the person who had influenced him most was Besicovitch, 'whose brilliant lectures on Analysis were a delight'.

R.A. Rankin, sometime professor of mathematics at Glasgow, 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'.

Civil service, 1940-1945

In early 1940, Pat obtained a job as experimental officer in the Ministry of Supply. He was appointed to the Projectile Development Establishment (rockets!), then at Fort Halsted in Kent and later (from May 1940) near Cardigan in Wales. The group included D.G. Kendall (later professor at Cambridge), whom he met for the first time in the lift on the way to the job interview, and M.S. Bartlett (later professor at Manchester, London and Oxford), together with others such as J. Howlett (later head of the Atlas Computer Laboratory at Harwell), R.A. Rankin (later professor of mathematics at Glasgow), G.J. Whitrow (later professor of the history of science at Imperial College) and N.B. Slater (later professor of mathematics at Hull). He found the work uninteresting, however, and sought a transfer to the External Ballistics Laboratory in Cambridge to which he moved in February 1941. This turned out to be worse as they were 'only given routine calculations to do, and not allowed to see any secret research reports'.

Pat joined the Australian Scientific Liaison Office (ASLO), run by the CSIR, in London in late 1943, through the good offices of C.S. Davis who had been a fellow science student in Sydney and was later professor of mathematics at the University of Queensland. At the time, Davis was acting as liaison officer for operational research, after completing two tours of operations as a fighter pilot and attaining the rank of Wing-Commander, but he was being posted back to Australia. Pat was appointed to provide the liaison on general physics and operational research (with some radar). At first he was sent to do a seven-week course in radar at Malvern, whose head of school was L.G.H. Huxley (later Vice-Chancellor of the ANU). This he enjoyed thoroughly and the next two and a half years which he spent in this office 'were the most valuable scientific experience [he] ever had'. He covered a great diversity of applied physics including vision, camouflage, army signals, quality control, road research, infra-red detection, metrology, UHF radio propagation, general radar, bomb-fragmentation, rockets and asdics. More valuable to him later, however, was the operational research and associated subjects. Every few months he visited each of the operational research sections in Fighter, Coastal, Bomber, Tactical and Training Commands and he was also accredited to the US Bomber, Fighter and Tactical Air Force Commands. He wrote up what they were doing and sent his reports, 122 in all, to CSIR, the RAAF and the Australian Army Headquarters in London. He was also an observer to quite a number of Ministry of Supply committees, some of which were very instructive and run in the style of a research seminar.

This time in the Liaison Office marked the beginning of Pat's research activities. The paper on convex bodies was concerned with measuring the mean projected area of a shell fragment and was instigated by D.G. Kendall. A special camera to use the method was built at the Safety in Mines Research Establishment at Buxton, which was responsible for much of the work on bomb fragmentation. In the late 1970s the CSIRO Division of Industrial Chemistry in Melbourne used the method for measuring the surface areas of very small particles with an electron microscope. Convex bodies and figures remained an abiding interest with Pat and an important part of his work on geometric probability.

Pat began greatly to regret his lack of statistical knowledge during the Liaison Office period. After the flying bomb attacks on London began in May 1944, he read Volume 1 of M.G. Kendall's  Advanced Theory of Statistics  'as an anodyne' and found it 'an eye-opener and an inspiration'. He began to work on rank correlation but found that Henry Daniels had anticipated his results in a paper just about to be published. He also joined the Royal Statistical Society, in whose library he read after lunch each day, and got to know M.G. Kendall with whom he was later to write a book on geometrical probability.

Pat also kept his interest in analysis alive during the war and wrote several papers on Hausdorff measure, as a result of the inspiration by A.S. Besicovitch. Indeed one of these ('The measure of product and cylinder sets',  J. London Math. Soc.  21, 175-179) was joint with Besicovitch who had discovered the result some three months earlier but generously suggested joint publication.

In June 1945 Pat left ASLO after being awarded the Baylis Research Studentship at St John's College, Cambridge. Pat wanted to be supervised by Besicovitch but to his surprise Besicovitch declined and suggested F. Smithies, who agreed. Smithies put Pat on to the problem of determining the nature of the set of points of divergence of Fourier integrals of functions in the class L^p, l<p<2. This was far too hard, however. Pat made no progress and indeed the problem remains unresolved. For pleasure he worked on statistical problems proposed to him by M.G. Kendall and J. Wishart.

Oxford, 1946-1951

After one year at Cambridge, Pat gave up his studentship and took up a position as Senior Research Officer at the Institute of Statistics at Oxford University. He had met Jean Mavis Frame (of Reading) in 1945; they decided to marry and he needed the extra income. The marriage took place on 14 September 1946 and the union produced three children: Everill Frances Louise (b. 1947), Michael Patrick Allan (b. 1950) and Hugh Frederick (b. 1953). They have, respectively, taken up careers in university administration, as a librarian, and as a keyboard musician. Pat never did acquire a PhD but was subsequently to receive an ScD degree from Cambridge and a DSc from Sydney.

The Institute of Statistics at Oxford was then housed in huts in the grounds of St Hugh's College. It shared this accommodation with the Bureau of Animal Population and the Edward Grey Institute of Ornithology. Pat used their library and talked to Charles Elton and P.H. Leslie of the former and David Lack of the latter. He was later to comment that 'this gave me an abiding interest in animal populations on which I wrote a number of papers, and from it learnt a great deal'. His influential paper on lynx cycles, inspired by discussions with Charles Elton, dates from this period together with four papers on animal populations. The paper ('The statistical analysis of the sunspot and lynx cycles',  J. Animal Ecology  18, 115-116) was later followed up by 'The statistical analysis of the Canadian lynx cycle I. Structure and prediction' ( Austral. J. Zool.  1, 163-173) and 'The statistical analysis of the Canadian lynx cycle II. Synchronization and meteorology' ( Austral. J. Zool.  1, 291-298), and the time series in the latter paper has been repeatedly and often mistakenly re-analysed by others. It is essentially a nonlinear process. Another paper, 'Some remarks on animal population dynamics' ( Biometrics 6, 250-258) provides a model which leads to 'chaotic' behaviour, a topic of great current interest, although Pat did not recognise this till some thirty years later. The papers 'The statistical analysis of game-bird records' (I) ( J. Animal Ecology 21, 154-158) and 'The statistical analysis of game-bird records (II)' ( J. Animal Ecology  23, 35-37), resulted from conversations with Lack.

Pat remained at Oxford until late 1951. He had been attached to Balliol College, although not as a Fellow. Later he lectured at Trinity College (1949-51) and was made a University Lecturer in 1951.

Professor at ANU, 1952-1982

Pat moved to Canberra at the beginning of 1952 as foundation professor of statistics at the Australian National University. The University then was still in its infancy. It had been launched in 1949 with aspirations to compare favourably with high-quality overseas universities, to secure Australia a place in international research, and to attract back to Australia some of the many expatriates who had made names for themselves abroad. It was intended that, by pursuing research at the highest level, ANU would set new standards and provide advanced training to fulfil national needs for qualified personnel.

It was the Research School of Social Sciences (RSSS) at ANU that first saw the need for a Department of Statistics. Pat had no background in the social sciences but at Oxford he had associated with the economist Richard Stone, later a Nobel laureate, and RSSS may have thought that he had a particular interest in the area. This was not the case, but RSSS generally remained tolerant of his mathematically orientated endeavours.

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. At the time of Pat's death, nine of the fifteen professors of statistics then serving in Australian universities had been associated with his department, either as staff or students. Pat himself had been involved with the supervision of twenty PhD students.

Pat's first recruits were the PhD students E.J. Hannan (FAA 1970) and J. Gani (FAA 1976) and he was later to write that 'I do not know of any professor who had the good fortune to start off with two research students of such astonishing capacity'. Later he made a sequence of high-quality academic appointments, beginning in 1955 with G.S. Watson, subsequently professor of statistics at Princeton University.

Soon after Pat came to Canberra, he published the paper ('A probability theory of dams and storage systems',  Austral. J. Appl. Sci.  5, 116-124) that marked the beginning of the stochastic study of dam theory. It was later discovered that a Russian hydrologist, Savarensky, had written down the same key equations in 1940 or earlier, but apparently he did not recognize that they defined a Markov chain. Pat made a considerable reputation, both in statistics and hydrology, for his work in the area. This included the influential book  The Theory of Storage  published in 1959.

Pat was elected to the International Statistical Institute (ISI) in 1966 and he subsequently played a significant part in its activities, serving as vice-president for the periods 1971-1973 and 1975-1977. He was chairman of the Program Committee, a quite onerous task, for the 40th Session in Warsaw in 1975 and the 41st Session in Delhi in 1977. He was also a member of the council of the ISI's International Association for Statistics in the Physical Sciences, 1967-1971. In all, Pat attended eight ISI Sessions: Sydney 1967, London 1969, Washington 1971, Vienna 1973, Warsaw 1975, Delhi 1977, Manila 1979, and Madrid 1983.

The paper 'Random processes in genetics' ( Proc. Camb. Phil. Soc.  54, 60-71), published in 1958, was Pat's first attempt at a genetic problem and was inspired by W. Feller's article in the Proceedings of the Second Berkeley Symposium. He quickly developed expertise in the area and, after a flurry of activity, produced the book  The Statistical Processes of Evolutionary Theory  in 1962. Subsequently he continued to publish in the area but decreasingly to concentrate on it.

Of Pat's original students, E.J. Hannan, who arrived in 1953, remained in the Department until January 1959 when he was appointed to the chair of statistics at the (then) Canberra University College which became the School of General Studies of the ANU in 1960. Hannan returned to Pat's Department as a professor in 1971 and remained throughout Pat's tenure as a close colleague.

The other original student, J. Gani, returned to the Department as a Senior Fellow in 1960 and remained until 1964. He had considerable disagreements with Pat over the administration of the Department and over the creation of the  Journal of Applied Probability  which Pat initially did not support. Relations were strained when Gani departed for the USA in 1964, but Pat was later to play a significant role in his appointment as Chief of the CSIRO Division of Mathematics and Statistics in 1974.

In 1962 Pat was elected to the Fellowship of the Australian Academy of Science and he was awarded the Academy's Lyle Medal in 1963. He served on the Council of the Academy during 1971-1974. He was Editor of the Academy's  Records  from 1979 to 1983 and oversaw the journal's successful transformation into  Historical Records of Australian Science.

At ANU Pat continued to develop his interests in geometric probability which had dated from his wartime work on coverage problems. The book  Geometrical Probability, with M.G. Kendall, published in 1963, was particularly notable. His work with S. Fazekas de St. Groth ('A mathematical model of virus-cell interaction'.  J. Hygiene  53, 291-296 and 'Random circles on a sphere'.  Biometrika  49, 389-396) on the random pattern of antibodies attached to a spherical virus displayed an unusual facet of his scientific talent. Simulated results were obtained from a suitable apparatus using spray paint and table tennis balls. Indeed, it is no accident that his reputation rests in fair measure on his founding of a school of applied probability. He was fascinated by science as such, and by nature was a scientist who was concerned both with the solution of specific problems and with general frameworks for the solution of classes of problems.

In 1963-64, Pat was first president of the newly formed Statistical Society of Australia. This had been created in October 1962 by the amalgamation of the Statistical Societies of New South Wales (founded 1947) and Canberra (founded 1961) which then became branches of the main Society. Further branches were later formed in Victoria (1964), Western Australia (1964), South Australia (1967) and Queensland (1981). Pat was an associate editor of the Society's  Australian Journal of Statistics  from 1963 to 1978. He became an honorary life member of the Society in 1978 and was awarded the Society's Pitman Medal for his research in 1982.

Pat was also active in a variety of other learned societies. He served as president of the Australian Mathematical Society in 1976-78. He became an Honorary Life Fellow of the Royal Statistical Society in 1970 and was elected to the Royal Society in 1975.

Pat served on many committees and enquiries over the years. Two of particular significance concerned the efficacy of rain-making experiments (about which he wrote in the paper 'The methodology of rain-making experiments (with discussion)'.  Rev. Internat. Statist. Inst.  38, 105-119) and the safety of the (then prospective) Australian National Animal Health Laboratory in Geelong where it was planned to keep live virus of the foot and mouth disease. (For some background on the latter see Courtice (1989).)

Pat became quite a close friend of Jerzy Neyman, founding father of the famous Department of Statistics at the University of California at Berkeley, and he visited Berkeley for a month in each of 1965, 1970 and 1971. His longer periods abroad, one year each in 1955-56 and 1960, were spent in Oxford.

Pat retained the Headship of the Department of Statistics throughout his tenure at ANU. He rarely sought to exercise power but he was reluctant to share it.

Emeritus years, 1983-1988

Pat formally retired from his Chair at the end of 1982, the year in which he turned 65, but he stayed on at ANU as an honorary Visiting Fellow in the NH&MRC Social Psychiatry Research Unit. There he provided advice on statistical methods and published a number of papers on epidemiological methods. He had a long-standing interest in psychiatry and mental disorders and published, for example, eleven papers in the  British Journal of Psychiatry  during the twenty-year period 1966-1986.

Amongst his papers in this area are several written jointly with E.H. Hare, a consultant psychiatrist at the Maudsley Hospital, London. They deal with seasonality of birth in the psychoses and other disorders, birth order, and the effects of maternal and paternal age. The initial papers were written by correspondence without the authors having met.

After his retirement Pat came periodically to his old department to collect mail, but he avoided seminars and more formal academic contact. This was much to the regret of his statistical colleagues who greatly valued his insights and encyclopedic knowledge.

Pat suffered a stroke in July 1987 which paralysed his left side. This setback did not quench his intellectual activity and he slowly improved in condition with devoted support from his wife Jean. However, a heart attack on 19 September 1988 ended his life.

Personal

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.

He was notable for his contemplative wisdom, pipe in hand, and for his virtuosity with penetrating one-line phrases. A sample retort he quotes concerns his response to a Canadian woman's first conversational gambit at a conference cocktail party. Her query of 'Are you a full professor?' was countered with 'No, I've only had one beer so far'.

Another memorable characteristic of Pat's was his husky voice. This dated from his childhood when 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 Joe Gani's words, 'he was the sort of person with whose views one could disagree violently on occasion, while retaining one's respect for his dedication to research, and one's human affection for him'.

Additional personal biographical notes

(i) Contributed by D.G. Kendall, FRS

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 gauche embarrassment. We instantly became great friends.

When we reported for duty I came stripped for action, but Pat with greater foresight brought with him several mathematical books, a set of the  Encyclopaedia Britannica, and a bottle of Irish whiskey. The gang of strangers at the interview turned out to consist mostly of recent Cambridge undergraduates who knew far more than I did on almost every topic except perhaps Fourier integrals and astrophysics, neither of which were much in demand at that time. So I learned a lot from them, and especially from Pat. I recall an argument about how one should describe the noise of a rocket firing. Moran said wisely, 'it's exactly like the tearing of silk underwear'. This made a great impression.

Pat was full of things he had learned from A.S. Besicovitch and from Frank Smithies. In particular he introduced me to geometrical probability, later to be very important to us both. Neither of us knew any statistics.

He was very proud of his surname with its suggestion that he might be the second most dangerous man in London. This was stressed one evening when he invited me to join him at a local pub to meet a naval officer called Moriarty.

Eventually we were pointed in different directions so I didn't see him for several years, but it was a great pleasure on my return to Oxford in 1946 to find Pat based in the Institute of Statistics and busy with research on time series. We set up a joint seminar, mainly to educate ourselves but featuring from time to time eminent figures like Maurice Bartlett, Sir Cyril Hinshelwood, and A.S.C. Ross who was then busy with probability problems in linguistics. We also enjoyed the stimulus of working beside David Champernowne, David Finney, and P.H. Leslie.

One evening Pat took me to a meeting of the Newman Society atwhich he was due to give a talk on Lysenko. He took pains to make the point that Lysenko's disagreements with other scientists were not necessarily a consequence of his Marxist views. 'Indeed', said Pat, 'there are perhaps things that the Church could learn from Marxism' Some were startled by this remark. When I reminded Pat of the incident many years later, he insisted that he  could not  have said such a thing. But he did, and it was a prophetic saying.

Pat was thrilled when the call came for him to set up a Department of Statistics in Canberra, and there is no doubt at all that this challenge broadened his thinking and caused his work to open out in numerous fresh directions. In particular he now took up genetics seriously and made famous contributions to that subject.

After this we met only every four years or so, but he always had something fresh and exciting to say about his researches.

Moran's father had enjoyed an adventurous life and wrote several books about it. He died in Cambridge some time before I took up a post there in 1962, and second-hand copies of these kept turning up on David's book-stall in the market. I purchased all I could find, and despatched them to Canberra. They were interesting books. Did Pat never feel tempted to follow his father's example? It would have been fascinating to read his indiscreet revelations.

Pat was well read in St Thomas Aquinas and would often seize the attention of a dinner party with some apposite quotation. When conversation seemed to be drying up, he could revive it by reading from a little black book his list of people whose surnames described their actual occupations. He was pleased when I sent him a notice of a meeting of the Friends of Ripon Cathedral that said, 'we are happy to announce a lecture on our beloved church by the noted ecclesiastical architect, Dr Buttress'.

Because of Pat's frequent quotes from St Thomas I assumed without checking that he was a Latinist, and this is why my contribution to his  Festschrift  contained an appendix in that language. It turned out that I was mistaken – and fortunately so because my Latin contained a dreadful howler.

Pat and I were much of an age, but he had the advantage of a year or two so I came to think of him as a very slightly older brother. If he had been such, I could not now treasure his memory – and miss him – more than I do.

(ii) Contributed by M.S. Bartlett, FRS

David Kendall, in his lively recollections of Pat Moran, mentions their first meeting when joining a team of mathematicians working on rocket weapons research during the war. I had already jointed William Cook's theoretical group as a statistician, but as Pat did not become 'sold' on statistics until after the war, our interests did not particularly interact until 1945-6, when Pat returned to Cambridge as a student and I as a lecturer. I do not recall Pat there, but presumably he did for a time attend some of my lectures; at any rate, he showed me much later a set of notes of my lectures that he seemed to hold in some esteem.

Our paths soon diverged, for Pat went to Oxford and I to Manchester, where I was when he returned to Australia to take up the Canberra Chair. Some contact between us obviously developed, for Pat's little monograph published in 1959 on the theory of storage was one of the first that I edited for the new Methuen series of monographs on applied probability and statistics. However, I do not recall our paths actually crossing again until the summer of 1967, just before I myself moved to Oxford, when an International Statistical Institute session in Sydney brought me to Australia for the first time. After the conference I took the opportunity to visit Canberra, I think at the same time as C.R. Rao, and Pat personally escorted us round the university campus and its environs. Six years later, when I had qualified for my one and only entire sabbatical year, Pat invited me to spend it in his department in Canberra as a Visiting Fellow, and procured a university dwelling for my wife Sheila and myself in the campus grounds. We thus got to know Pat and his wife Jean well. It was unfortunate that our stay soon became marred by my own illness and hospitalisation, but this cannot affect the pleasant memories I have of Pat, his family and his professional colleagues. During my spell of convalescence in the Christmas vacation, Pat and Jean arranged a holiday for the four of us at the coastal resort of Ulladulla east of Canberra. One must always be prepared in Australia for sudden invasions by strange creatures like flying beetles or whatever. On this occasion the beach was littered with 'Portuguese men-of-war' whose long stinging tentacles can be something of a menace in the water; this no doubt contributed to a disinclination of my wife and myself to bathe, but I do not remember any such nervousness by Pat and Jean.

I naturally renewed my personal contacts with Pat on two later visits to Australia, even though these were primarily arranged by CSIRO. In 1981 Pat and Jean made an extensive visit to England, and my wife and I were delighted to have them stay with us for a day or so in Totnes, Devon, where in my retirement I was then living. Pat was very keen to trace some of his ancestors in England, and we went to the church at Broadhempston a few miles away where some tombstones bearing the family name (on his mother's side) were discovered.

Pat's visit to England was, as Jean recently reminded me, a very comprehensive one professionally, made as a Senior Research Fellow of the Science Research Council. He gave lectures or seminars at Bath, Cambridge, Edinburgh, London, Manchester, Newcastle, Oxford and Rothamsted, and renewed his contacts with his many colleagues in the UK. Of these I will mention specially only J.K. Wing and E.H. Hare, they being associated with Pat's interests in psychiatric research in his later years.

1982 saw Pat's official retirement from his Canberra Chair, but this did not halt his flow of publications which continued until 1988. Even his stroke in 1987 he combated courageously with his wife's support. In a short letter to me as late as 13 February 1988, he wrote: 'I am getting on slowly and steadily and feel very optimistic about the future.... Obviously my work goes slowly but I am still doing a little'. It was thus a shock to us all to hear of Pat's death from heart failure later in 1988.

Some notes on Pat Moran's contribution to mathematical statistics and biomathematics

Contributed by M.S. Barlett, FRS

Pat Moran's election to the Chair of Statistics at the Australian National University in Canberra in 1952 occurred comparatively early in his career and, while it greatly stimulated the development of theoretical statistics in Australia, it to some extent separated him from the greater number of his contemporaries in the western world, with the consequent risk that his research contributions were not always appreciated. In spite of my own long acquaintance with many aspects of his researches, it was perhaps not until I re-examined his complete bibliography that I was able to grasp fully the range and depth of his work.

An enumeration by numbers is not the best way to indicate this but, before any areas of interest are commented on in more detail, it is helpful to note something of the structure in time and subject. Thus of over 170 publications listed in his bibliography, there were four books, viz. (in chronological order):

1. The Theory of Storage  (Methuen, London, 1959; translated into Russian, 1963; Czech, 1967).
2. The Statistical Processes of Evolutionary Theory  (Clarendon Press, Oxford, 1962; translated into Russian, 1973).
3. (With M.G. Kendall)  Geometrical Probability  (Griffin, London, 1963; translated into Russian, 1972).
4. An Introduction to Probability Theory  (Clarendon Press, Oxford, 1967).

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'.

A more specific attack on that part of applied probability theory arising in population evolutionary genetics is represented by b). It presents an account of the theory as far as it had developed at the time, with the most numerous references inevitably going to the work of the three well-known pioneers in this field, R.A. Fisher, J.B.S. Haldane and Sewall Wright. Moran's eleven references to his own original work come next in number, equalling.those to the work of Motoo Kimura (both authors having many further publications in population genetics after 1962). The total number of research papers published by Moran in this field is around 35 (excluding those classifiable under psychiatry), this number exceeding that of Moran's in any other field except the general field of statistical inference, where it reaches around 50. This helps to indicate the considerable time and energy that Moran devoted to population genetics. From a remark he once made to me, he was a little disappointed that his book did not achieve wider recognition. This is possibly explained – without, however presuming to assess the biological import of his book – by his strict adherence to his avowed aim of providing a rigorous account of a subject in which the chief protagonists had not always been so careful. There is, moreover, an unavoidably incomplete resolution in it of some of the problems that came to light, several of which Moran resolved in later research.

Thus, while it was known to both Fisher and Sewall Wright (and noted by Moran in his book) that Fisher's 'Fundamental Theorem of Natural Selection', that mean fitness from one generation to another never decreased, was no longer true for frequency-dependent selection, an important further contribution was made by Moran in 1964 'on the non-existence of adaptive topographies'. Moran showed that Fisher's 'theorem', which Fisher had established for a single gene-locus model, did not necessarily extend to a two-loci model.

Some of Moran's later papers in population genetics (e.g. in 1975 and 1976) investigated the theory of population models of electrophoretically detectable genetic variation. (For a comparatively recent discussion of this topic, see Chapter 8 of M. Kimura's 1983 book,  The Neutral Theory of Molecular Evolution.)

A topic that was discussed by Moran in his 1962 book was the effect of subdivision of the total population into a number of sub-populations with intermigration. He found that in the absence of selection (and mutation) the subdivision had little effect on the population's rate of approach to homozygosity even for quite low migration rates; in contrast, if there were selection forces heterogeneous over the sub-populations and acting in different directions, these could have a very large influence in delaying homozygosity.

Before moving to Canberra, Pat Moran occupied a post at Oxford University's Institute of Statistics from 1946 to 1951. Although the activities of this Institute were primarily economic, a liberal attitude to the responsibilities of the occupant of this particular post enabled Moran during this period to begin his research studies in ecology, including statistical capture-recapture sampling methods and the analysis of the Canadian lynx cycle and other time-series; also his various more general investigations in stochastic processes and statistical inference.

An interesting ecological paper is his 1960  Biometrics  paper on animal population dynamics, where his general theoretical discussion includes some on the discrete population model n_i+1 = F(n_i). He remarks:

That stable cycles can exist with suitable chosen F(x) can be easily shown mathematically. I have carried out numerical and mathematical investigations on a number of such functions which verify this conclusion...

As R.M. May has noted ('Chaos and the dynamics of biological populations',  Proc. Roy. Soc., A, 413 [1987], 27-44), the above model can also lead to 'chaotic behaviour', but the implications of this for actual systems, whether physical or biological, was not appreciated until later, when emphasized by May and his contemporaries.

Moran's contributions to the general area of statistical inference, while numerous, are somewhat miscellaneous, and only one or two of the topics not already mentioned are singled out here for comment. The first is the problem of inference, not for the relatively familiar domain of stationary time-series but for other stochastic processes of an 'evolutive' character. In his 1961 and 1953 papers in the  Journal of the Royal Statistical Society  in this area, Moran stressed in particular the relevance of the 'stop rule' in discussing the estimation of parameters for the birth-and-death process and other simple processes.

An important general paper classifiable under the Neyman-Pearson theory of testing statistical hypotheses was Moran's 1970  Biometrika  paper, 'On asymptotically optimal tests of composite hypotheses'. Neyman had developed what he termed C(a) tests for testing the null hypothesis q₁ = 0 against the alternative q₁ ¹ 0 when further parameters q₂, ... q_k are unknown, given a sample of  n  independent observations on a (possibly multivariate) random variable X with distribution, say, F(X | q). Moran showed that Neyman's C(a) tests are asymptotically equivalent to the use of the likelihood ratio test and to tests using the maximum likelihood estimators; and he re-examined the conditions for C(a) tests to be asymptotically optimal.

References

This memoir draws heavily on Pat Moran's unpublished autobiographical notes:  My Family  (dated 31 March 1976),  Memories  (31 March 1976),  The Australian Scientific Liaison Office, London, 1943-45  (3 August 1982) and  Notes on My Papers  (3 August 1982). These are held in the Basser Library of the Australian Academy of Science. All quotations are taken from these sources unless otherwise indicated.

Courtice, F.C., 'Bede Morris, 1927-1988',  Hist. Records Austral. Science,   8 (1989), 15-36.

Gani, J., 'Patrick Alfred Pierce Moran, 1917-1988',  Bull. Inst. Math. Statist.,  17   (1988), 449.

Gani, J. and Hannan, E.J., (eds.),  Essays in Statistical Science  (1982) ( J.   Appl. Prob.,  Special Volume 19A).

Hall, P.G., 'Obituary: Patrick Alfred Pierce Moran, 1917-1988',  Biometrics, 45   (1989), 687-692.

Hannan, E.J., 'Some memories of Pat Moran',  J. Appl. Prob.,  6   (1989), 215-218.

Heyde, C.C., 'Patrick Alfred Pierce Moran. Died 19 September 1988, Elected to Fellowship 1962',  Australian Academy of Science Year Book, 1990-91, p. 81.

Smith, C.A.B., 'Obituary: Pat Moran, 1917-1988',  J. Roy. Statist. Soc.,  A, 152 (1989), 419.

Acknowledgements

Thanks are due to P.O. Bishop, D.J. Daley, J.M. Gani, E.J. Hannan, R.W. Home, M.R. Osborne, J.R. Philip and R.A. Rankin for comments and suggestions and to M.S. Bartlett and D.G. Kendall for their contributions.