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SUMMARY:Ferguson's 1973 paper on the Dirichlet process - University of Cam
 bridge
DTSTART:20090225T163000Z
DTEND:20090225T173000Z
UID:TALK17111@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:In 1973\, Ferguson proposed to perform nonparametric estimatio
 n in a Bayesian\nframework by defining a prior distribution on an infinite
 -dimensional\nparameter space (the set of probability measures\nover a giv
 en domain). When applied to a finite set of observations\, only a\nfinite 
 number out of the infinitely many degrees of freedom is used to\nexplain t
 he data\, which accounts for the term "nonparametric". The prior\nmodel is
  constructed as a stochastic process\, with Dirichlet marginals and\npathe
 s in the set of probability measures over a separable metric space\,\nthat
  Ferguson called a "Dirichlet process". His estimation model has a\nconjug
 ate form with a closed-form solution for the posterior parameters\,\nwhich
  mimics the conjugate posteriors of the Dirichlet marginals under a\nmulti
 nomial sampling model. Measures drawn at random from the\nDirichlet proces
 s are a.s. discrete.\n\nI will review Ferguson's construction and his appl
 ication of the model to\nsample observations. I also intend to briefly dis
 cuss the two major lines of\nresearch which developed from Ferguson's pape
 r: One that attempts to\novercome the model's discreteness in order to con
 struct "universal" priors\,\nand one that exploits\ndiscreteness to genera
 lize the notion of finite mixtures and related models.\n\nArticle: http://
 www.ams.org/mathscinet-getitem?mr=350949\n\nTS Ferguson\, "A Bayesian anal
 ysis of some nonparametric problems"\nAnn. Statist. 1 (1973)\, 209--230.\n
LOCATION:MR5\, CMS
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