Probability Approximations Via the Poisson Clumping Heuristic

by David J. Aldous

Book Overview

If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 1441930884
• ISBN13: 9781441930880
• Release Date: December 2010
• Publisher: Springer
• Length: 272 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"

Customer Reviews

a different approach to probability

I did my Ph.D. dissertation on extreme value theory for stationary stochastic processes. My work got me interested in a parameter called the extremal index and a colleague, Tai Hsing once showed me how the extremal index was related to the frequency with which a stochastic process crosses a high or low level. An extremal index less than one corresponds to clumping and the point process defined by the high level crossings is approximately Poisson. Hsing was a student of Leadbetter. Hsing and Leadbetter exploited this idea in their publications and Leadbetter explains some of it in his 1983 book with Lindgren and Rootzen. I eventually published a paper with Tai Hsing and Bill McCormick where we further investigated properties of the extremal index and Tai contributed using this "Poisson Clumping Heuristic" that Aldous writes about in this monograph. My other connections to topics in the book include my exposure to geometric probability from Herb Solomon as a graduate student at Stanford. Also I knew Charles Stein while I was a Stanford student and I learned to appreciate the power of a tool called "Stein's method" from lectures by Diaconis. A student of Stein's by the name of Chen had gotten a Ph.D. in statstics at Stanford utilizing the Stein method. Aldous ties all these themes together in this very interesting monograph. It uses heuristics, so we do not see mathematical proofs. But the text is at a high level and refers the reader to advanced literature. For graduate students in probability or statistics it is a great source for finding a thesis topic (even today with the book 12 years old). For researchers in extreme value theory, geometric probability or probability theory in general it is a great reference source.