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P. A. P. Moran

P. A. P. Moran is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand P. A. P. Moran rather than just read about it. In short: Patrick Alfred Pierce Moran FRS (14 July 1917 – 19 September 1988) was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics. Early years Patrick Moran was born in Sydney and was the only child of Herbert Michael Moran (b. 1885 in Sydney, d. 1945 in Cambridge UK), a prominent surgeon and captain of the first Wallabies, and Eva…

P. A. P. Moran — main illustration
P. A. P. Moran — illustration

Key takeaways

  • P. A. P. Moran belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect P. A. P. Moran to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of P. A. P. Moran from memory before moving on to harder problems.

Reference excerpt

Patrick Alfred Pierce Moran FRS (14 July 1917 – 19 September 1988) was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics.

Early years Patrick Moran was born in Sydney and was the only child of Herbert Michael Moran (b. 1885 in Sydney, d. 1945 in Cambridge UK), a prominent surgeon and captain of the first Wallabies, and Eva Mann (b. 1887 in Sydney, d. 1977 in Sydney). Patrick did have five other siblings, but they all died at or shortly after birth. He completed his high school studies in Bathurst, in three and a half years instead of the normal five-year course. At age 16, in 1934, he commenced study at the University of Sydney where he studied chemistry, math and physics, graduating with first class honours in mathematics in 1937. Following graduation he went to study at Cambridge University from 1937 to 1939, his supervisors noted that he was not a good mathematician and the outbreak of World War II interrupted his studies. He graduated with an MA (by proxy) from St John's College, Cambridge, on 22 January 1943 and continued his studies there from 1945 to 1946. He was admitted to Balliol College, Oxford University, on 3 December 1946. He was awarded an MA, from Oxford University, by incorporation in 1947.

Career During the war Moran worked in rocket development in the Ministry of Supply and later at the External Ballistics Laboratory in Cambridge. In late 1943 he joined the Australian Scientific Liaison Office (ASLO), run by the CSIRO. He worked on applied physics including vision, camouflage, army signals, quality control, road research, infra-red detection, metrology, UHF radio propagation, general radar, bomb-fragmentation, rockets, ASDICs and on operational research. He also wrote some papers on the Hausdorff measure during the War. After the war, Moran returned to Cambridge where he was supervised by Frank Smithies and worked unsuccessfully on determining the nature of the set of points of divergence of Fourier integrals of functions in the class Lp, when 1 < p < 2. He gave up on this project and was employed as a senior research officer at the Institute of Statistics at Oxford University. He also gave lecture courses. Patrick Moran was appointed university lecturer in mathematics in 1951, at Oxford, without stipend, for as long as he held the post of senior research officer in the Institute of Statistics. Moran freely admitted he had difficulty with simple arithmetic and wrote that, "Arithmetic I could not do". He married in 1946 after his appointment; he and his wife Jean Mavis Frame had three children, Louise, Michael and Hugh. At Oxford Moran wrote several papers on the nonlinear breeding cycle of the Canadian lynx. He was made a lecturer at Oxford in 1951 but left the university later that year for Australia. He never acquired a PhD, "a fact he would recall with some pride in later life", recalls Hall. On 1 January 1951, Moran was appointed foundation professor of statistics in the Research School of Social Sciences at the Australian National University in Canberra. He worked on the stochastic study of dam theory, and on population genetics, publishing his first paper "Random processes in genetics" in the Proceedings of the Cambridge Philosophical Society in 1958 and culminating in his 1962 book The Statistical Processes of Evolutionary Theory. He also worked on geometric probability. In 1963, he was awarded the Thomas Ranken Lyle Medal by the Australian Academy of Science. He retired from ANU at the end of 1982; he stayed on as Emeritus Professor and worked on statistical methods in particular epidemiological methods and their application to psychiatry. He was awarded an honorary ScD degree from Cambridge, on 29 October 1963, and a DSc from Sydney. He was made a Fellow of the Royal Society in 1975. Moran died after a stroke in 1988. The P.A.P Moran Building (Building 26B) at A.N.U. was named in his honour. It houses offices of the Mathematical Sciences Institute, tutorial rooms and the Research School of Economics. The Moran Medal, created in his honour, is awarded by the Australian Academy of Science every two years for distinguished work in statistics by an Australian statistician.

See also Moran's I Moran process Moran's theorem

Publications In addition to over 170 papers, Moran wrote four books,

The Theory of Storage (1959; translated into Russian, 1963; Czech, 1967) The Statistical Processes of Evolutionary Theory (1962; translated into Russian, 1973) (With M.G. Kendall) Geometrical Probability (1963; translated into Russian, 1972) An Introduction to Probability Theory (1967)

References

External links Heyde, C.C. (1992). "Patrick Alfred Pierce Moran 1917–1988". Historical Records of Australian Science. 1: 17–30. doi:10.1071/hr9920910017. Archived from the original on 1 January 2007. Hall, P. G. (1989). "Obituary: Patrick Alfred Pierce Moran 1917-1988". Biometrics. 45 (2): 687–692. JSTOR 2531511. For Moran's PhD students see: P. A. P. Moran at the Mathematics Genealogy Project Moran sent his first paper to R. A. Fisher: Correspondence of Sir R.A. Fisher: Calendar of Correspondence with P.A.P. Moran MS 018 – MORAN, Patrick Alfred Pierce, Manuscript collection, Basser Library, Australian Academy of Science The Moran Award for History of Science Research, Basser Library, Australian Academy of Science E Seneta; G K Eagleson (2004). "7. Henry Oliver Lancaster and the Australian Academy of Science" (PDF). Historical Records of Australian Science. 15 (2). CSIRO Publishing: 236–237. doi:10.1071/hr04005. Archived from the original (PDF) on 4 September 2012. Retrieved 16 June 2012.

Worked examples

Example 1 — a first encounter with P. A. P. Moran

Start with the simplest possible case. Write down what P. A. P. Moran claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to P. A. P. Moran before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about P. A. P. Moran ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of P. A. P. Moran

In research
P. A. P. Moran appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses P. A. P. Moran in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
P. A. P. Moran is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1917 births, 1988 deaths, 20th-century Australian statisticians, so understanding it makes those chapters shorter.
In everyday life
Look for P. A. P. Moran outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study P. A. P. Moran in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what P. A. P. Moran means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain P. A. P. Moran out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is P. A. P. Moran in simple terms?

Patrick Alfred Pierce Moran FRS (14 July 1917 – 19 September 1988) was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics. Early years Patrick Moran was born in Sydney and was the only child of Herbert Mich…

Why does P. A. P. Moran matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study P. A. P. Moran?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on P. A. P. Moran.

Tags

  • 1917 births
  • 1988 deaths
  • 20th-century Australian statisticians
  • Alumni of St John's College, Cambridge
  • Australian fellows of the Royal Society
  • Biostatisticians
  • Fellows of the Australian Academy of Science
  • Probability theorists
  • Scientists from Sydney
  • Spatial statisticians

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