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SUMMARY:Bayesian semiparametrics with Gaussian process priors - Ismael Cas
 tillo (CNRS and Paris 6)
DTSTART:20110204T160000Z
DTEND:20110204T170000Z
UID:TALK28653@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:In this talk we will first give a brief introduction to the Ba
 yesian nonparametric approach. Given a model\nparametrized by an unknown f
 unction or high dimensional parameter\, one puts an a priori probability\n
 distribution on it and studies the posterior distribution\, that is the co
 nditional distribution starting from\nthe prior and given the data. Then w
 e will move to the question of estimation in semiparametric models in a\nB
 ayesian way.\n\nA semiparametric model typically consists of a parametric 
 part of interest and a nonparametric part called\nnuisance. Putting a prio
 r distribution on both\, we are interested in the behavior of the marginal
  of the\nposterior with respect to the parameter of interest. A desirable 
 convergence result is the so-called\nBernstein-von Mises theorem\, which a
 sserts that the marginal posterior asymptotically converges to a normal\nd
 istribution centered at an efficient estimator.\n\nWe will discuss a set o
 f sufficient conditions to obtain this result\, mostly focusing on the cas
 e where the\nprior on the nonparametric part is a Gaussian process. An imp
 ortant role is played by the way the model is\napproximated through the Re
 producing Kernel Hilbert space of the prior. We illustrate the result on a
  few\nexamples\, including Cox proportional hazards model and a problem of
  alignment of curves. In particular\, we\nwill see that not all reasonable
 -looking nonparametric priors lead to good semiparametric properties.\n\n\
 nhttp://www.proba.jussieu.fr/~castillo/
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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