# Probability Approximations Via the Poisson Clumping Heuristic (Applied Mathematical Sciences)

Probability Approximations Via the Poisson Clumping Heuristic (Applied Mathematical Sciences)

Springer-Verlag Berlin and Heidelberg GmbH Co. K | 1989-12-31 | ISBN: 3540968997 | 269 pages | File type: PDF | 1 mb

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.

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