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CATEGORIES:Statistics
SUMMARY:Projective Limits of Bayes Equations - Peter Orban
z (Dept. Engineering\, Cambridge)
DTSTART;TZID=Europe/London:20081128T160000
DTEND;TZID=Europe/London:20081128T170000
UID:TALK14946AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14946
DESCRIPTION:Bayesian nonparametric models are essentially Baye
sian\nmodels on infinite-dimensional spaces. Most
work along\nthese lines in statistics focusses on
probability models\nover the simplex. In machine l
earning\, the problem has recently\nreceived much
attention as well\, and attempts\nhave been made t
o define models on a wider range of\ninfinite-dime
nsional objects\, including measures\, functions\n
and infinite permutations and graphs.\n\nIn my tal
k\, I will discuss the construction of nonparametr
ic Bayesian\nmodels from finite-dimensional Bayes
equations\,\nanalogous to Daniell-Kolmogorov exten
sion of measures to their\nprojective limits. I wi
ll present an extension theorem\napplicable to reg
ular conditional probabilities. This can be\nused
to guarantee that "conditional" properties of the\
nfinite-dimensional marginal models\, such as conj
ugacy and sufficiency\,\ncarry over to the infinit
e-dimensional projective limit model\, and to\ndet
ermine the functional form of the nonparametric Ba
yesian posterior\nif the model is conjugate.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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