The ubiquitous ewens sampling formula

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalStatistical Science
Volume31
Issue number1
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

  • Bayesian nonparametrics
  • Chinese restaurant process
  • Clustering
  • Coalescent process
  • Cyclic product distribution
  • Dirichlet process
  • Ewens's sampling formula
  • Ewens-pitman distribution
  • Exchangeability
  • Inductive inference
  • Logarithmic combinatorial structures
  • Permanental partition model
  • Poisson-dirichlet distribution
  • Random partition
  • Stick breaking
  • α-permanent

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