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SUMMARY:Projective Limits of Bayes Equations - Peter Orbanz (Dept. Enginee
 ring\, Cambridge)
DTSTART:20081128T160000Z
DTEND:20081128T170000Z
UID:TALK14946@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:Bayesian nonparametric models are essentially Bayesian\nmodels
  on infinite-dimensional spaces. Most work along\nthese lines in statistic
 s focusses on probability models\nover the simplex. In machine learning\, 
 the problem has recently\nreceived much attention as well\, and attempts\n
 have been made to define models on a wider range of\ninfinite-dimensional 
 objects\, including measures\, functions\nand infinite permutations and gr
 aphs.\n\nIn my talk\, I will discuss the construction of nonparametric Bay
 esian\nmodels from finite-dimensional Bayes equations\,\nanalogous to Dani
 ell-Kolmogorov extension of measures to their\nprojective limits. I will p
 resent an extension theorem\napplicable to regular conditional probabiliti
 es. This can be\nused to guarantee that "conditional" properties of the\nf
 inite-dimensional marginal models\, such as conjugacy and sufficiency\,\nc
 arry over to the infinite-dimensional projective limit model\, and to\ndet
 ermine the functional form of the nonparametric Bayesian posterior\nif the
  model is conjugate.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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