mathematics

Jim Pitman

Jim Pitman 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 Jim Pitman rather than just read about it. In short: Jim Pitman is a professor emeritus of statistics and mathematics at the University of California, Berkeley. Biography Jim Pitman (James W.

Key takeaways

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

Reference excerpt

Jim Pitman is a professor emeritus of statistics and mathematics at the University of California, Berkeley.

Biography Jim Pitman (James W. Pitman) was born in Hobart, Australia, in June 1949, son of E. J. G. Pitman and Elinor J. Pitman, daughter of W. N. T. Hurst. He attended the Hutchins School, Hobart, Australia from 1954 to 1966, then the Australian National University (ANU) in Canberra, from 1967 to 1970. He received a BSc degree from the ANU in 1970, followed by a PhD in probability and statistics in 1974 from the University of Sheffield, with advisor Terry Speed. He lectured at the Universities of Copenhagen, Berkeley and Cambridge, from 1974 to 1978, before joining Berkeley as an assistant professor in 1978. Following promotion to professor in 1984, he retired from teaching duties at Berkeley in July 2021. He is now emeritus professor of statistics and mathematics at the University of California, Berkeley. Pitman is a Fellow of the Institute of Mathematical Statistics, and is a past president (2007) of the institute. He was chief editor (1994—1996) of Annals of Probability.

Scientific work Pitman is known for his research in the theory of probability, stochastic processes and enumerative combinatorics. In particular, for long-running collaborations with Marc Yor on distributional properties of Brownian motion and Bessel processes, and with David Aldous on the asymptotics of random combinatorial structures and models for continuum random trees. With Lester Dubins, Pitman introduced the metaphor of the Chinese Restaurant Process for the scheme of adding new elements to a permutation by their insertion into previously formed cycles. His deeper study of this model, and its surprising relation with the theory of Brownian excursions led to the Pitman-Yor process as a model for random discrete distributions, and to generalizations of the Ewens's sampling formula including the Ewens-Pitman sampling formula. Much of his research is surveyed in his influential 2002 work, published as lecture notes at the Ecole d'Eté de Probabilités de Saint-Flour XXXII. In combinatorics, he is known for his elementary proof of Cayley's formula computing the number of spanning trees in a complete graph. This proof involving a double counting argument is noted for its elegance and appears in the book Proofs from THE BOOK.

Publications Pitman has published over 170 articles in mathematical journals. Among the most influential are:

Pitman, James W. (1975). "One-dimensional Brownian motion and the three-dimensional Bessel process". Advances in Applied Probability. 7 (3): 511–526. doi:10.2307/1426125. ISSN 0001-8678. "Pitman's theorem" commonly refers to Pitman's 1974 result that if B {\displaystyle B} is a standard one dimensional Brownian motion started at B 0 = 0 {\displaystyle B_{0}=0} , and M t = max 0 ≤ s ≤ t B s {\displaystyle M_{t}=\max _{0\leq s\leq t}B_{s}} , then 2 M − B {\displaystyle 2M-B} has the same distribution as B E S ( 3 ) {\displaystyle BES(3)} , the Bessel process which is the radial part of a 3-dimensional Brownian motion. Perman, Mihael; Pitman, Jim; Yor, Marc (1992-03-01). "Size-biased sampling of Poisson point processes and excursions". Probability Theory and Related Fields. 92 (1): 21–39. doi:10.1007/BF01205234. ISSN 1432-2064. Pitman, Jim (1995-06-01). "Exchangeable and partially exchangeable random partitions". Probability Theory and Related Fields. 102 (2): 145–158. doi:10.1007/BF01213386. ISSN 1432-2064. Pitman, Jim; Yor, Marc (1997-04-01). "The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator". The Annals of Probability. 25 (2). doi:10.1214/aop/1024404422. ISSN 0091-1798. Pitman, Jim (1993). Probability. Springer. doi:10.1007/978-1-4612-4374-8. ISBN 0-387-97974-3.

References

External links Home Page at U C Berkeley https://statistics.berkeley.edu/people/jim-pitman/ Recent publications https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=Pitman%2C+Jim&terms-0-field=author David Aldous. A Conversation with Jim Pitman Statist. Sci. 33(3): 458–467 (August 2018). DOI: 10.1214/18-STS656 https://projecteuclid.org/journals/statistical-science/volume-33/issue-3/A-Conversation-with-Jim-Pitman/10.1214/18-STS656.full Jim Pitman at the Mathematics Genealogy Project https://www.genealogy.math.ndsu.nodak.edu/id.php?id=30968

Worked examples

Example 1 — a first encounter with Jim Pitman

Start with the simplest possible case. Write down what Jim Pitman 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 Jim Pitman 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 Jim Pitman 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 Jim Pitman

In research: Jim Pitman 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 Jim Pitman 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: Jim Pitman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1949 births, 20th-century American statisticians, 20th-century Australian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jim Pitman 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 Jim Pitman in 20 minutes

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

Frequently asked questions

What is Jim Pitman in simple terms?

Jim Pitman is a professor emeritus of statistics and mathematics at the University of California, Berkeley. Biography Jim Pitman (James W.

Why does Jim Pitman 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 Jim Pitman?

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 Jim Pitman.