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SUMMARY:Learning rates in Bayesian nonparametrics - Aad van der Vaart (Vri
 je Universiteit Amsterdam)
DTSTART:20091126T140000Z
DTEND:20091126T153000Z
UID:TALK19990@talks.cam.ac.uk
CONTACT:Shakir Mohamed
DESCRIPTION:In semiparametric and nonparametric statistics the unknown par
 ameter is a function (e.g. regression function\, density).\n\nA Bayesian m
 ethod starts\, as usual\, by the specification of a prior distribution on 
 the parameter\, which is equivalent to modelling this function as a sample
  path of a stochastic process. Next Bayes' rule does the work and comes up
  with the resulting posterior distribution\, which is a probability distri
 bution on a function space.\n\nAfter giving examples of priors\, and discu
 ssing the way prior and posterior can be visualised\, we focus on studying
  the posterior distribution under the (nonBayesian) assumption that the da
 ta is generated according to some fixed true distribution.  We are interes
 ted in whether\, and if so how fast\, a sequence of posterior distribution
 s contracts to the true parameter if the amount of data increases.  We rev
 iew general results and examples\, including Gaussian process priors. The 
 general message is that\, unlike in parametric statistics\, a prior often 
 does not wash out\, and has a big influence on the posterior.\n\nThis depe
 ndence may be alleviated by another round of prior modelling\, focused on 
 a ``bandwidth'' parameter. The resulting hierarchical Bayesian procedures 
 can be viewed to provide an elegant and principled framework for regulariz
 ation and adaptation.\n
LOCATION:Engineering Department\, CBL Room 438
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