The ubiquitous Ewens sampling formula. (English) Zbl 1442.60010

Summary: Ewens’s sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory, algebra, and number theory. With an emphasis on its far-reaching influence throughout statistics and probability, we highlight these and many other consequences of Ewens’s seminal discovery.


60C05 Combinatorial probability
60G09 Exchangeability for stochastic processes
60G57 Random measures
62G05 Nonparametric estimation
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
92D15 Problems related to evolution
Full Text: DOI Euclid


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