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CATEGORIES:Statistics Reading Group
SUMMARY:Ferguson's 1973 paper on the Dirichlet process - U
niversity of Cambridge
DTSTART;TZID=Europe/London:20090225T163000
DTEND;TZID=Europe/London:20090225T173000
UID:TALK17111AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/17111
DESCRIPTION:In 1973\, Ferguson proposed to perform nonparametr
ic estimation in a Bayesian\nframework by defining
a prior distribution on an infinite-dimensional\n
parameter space (the set of probability measures\n
over a given domain). When applied to a finite set
of observations\, only a\nfinite number out of th
e infinitely many degrees of freedom is used to\ne
xplain the data\, which accounts for the term "non
parametric". The prior\nmodel is constructed as a
stochastic process\, with Dirichlet marginals and\
npathes in the set of probability measures over a
separable metric space\,\nthat Ferguson called a "
Dirichlet process". His estimation model has a\nco
njugate form with a closed-form solution for the p
osterior parameters\,\nwhich mimics the conjugate
posteriors of the Dirichlet marginals under a\nmul
tinomial sampling model. Measures drawn at random
from the\nDirichlet process are a.s. discrete.\n\n
I will review Ferguson's construction and his appl
ication of the model to\nsample observations. I al
so intend to briefly discuss the two major lines o
f\nresearch which developed from Ferguson's paper:
One that attempts to\novercome the model's discre
teness in order to construct "universal" priors\,\
nand one that exploits\ndiscreteness to generalize
the notion of finite mixtures and related models.
\n\nArticle: http://www.ams.org/mathscinet-getitem
?mr=350949\n\nTS Ferguson\, "A Bayesian analysis o
f some nonparametric problems"\nAnn. Statist. 1 (1
973)\, 209--230.\n
LOCATION:MR5\, CMS
CONTACT:Richard Samworth
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