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SUMMARY:Applications of Bernstein polynomials in Statistics - Sonia Petron
 e (University Bocconi Milan)
DTSTART:20101105T160000Z
DTEND:20101105T170000Z
UID:TALK25762@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:Bernstein polynomials are studied in analysis as a probabilist
 ic\napproximation scheme\, and they are well known to provide a constructi
 ve\nproof of Weirstrass theorem. In fact\, their simple probabilistic natu
 re make\nthem also attractive in many statistical problems.\nIn this talk 
 I will give an overview of applications of Bernstein\npolynomials in stati
 stics\, in particular in Bayesian nonparametric\ninference.\nI will briefl
 y review their use to construct a nonparametric prior\, which\nprovides a 
 smoothing of a Dirichlet process\, and allows to fairly easily\nincorporat
 e prior information. I will discuss theoretical properties and\nshow some 
 applications\, in particular to shrinkage estimation\, comparing\nwith the
  clustering properties of the Dirichlet process. Bernstein\npolynomials al
 so arise in quantile estimation from a Dirichlet process. I\nwill finally 
 discuss extensions to data on a general subset of R and to\nmultivariate d
 ata.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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