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SUMMARY:Postulating monotonicity in nonparametric Bayesian regression - El
 ja Arjas (University of Helsinki)
DTSTART:20100514T150000Z
DTEND:20100514T160000Z
UID:TALK24453@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:In situations where it can be applied\, an assumed\nmonotonici
 ty property of the regression function with respect to\ncovariates has a s
 trong stabilizing effect on the estimates. Because\nof this\, other parame
 tric or structural assumptions may not be needed\nat all. Although monoton
 ic regression in one dimension is well\nstudied\, the question remains whe
 ther one can find computationally\nfeasible generalizations to multiple di
 mensions. We propose a\nnonparametric monotonic regression model for one o
 r more covariates\nand a Bayesian estimation procedure. The monotonic cons
 truction is\nbased on marked point processes\, where the random point loca
 tions and\nthe associated marks (function levels) together form piecewise\
 nconstant realizations of the regression surfaces. The actual inference\ni
 s based on model averaged results over the realizations. The proposed\nmod
 el and estimation procedure is the first of its kind to combine the\nmonot
 onicity postulate with multiple covariates\, nonparametric model\nformulat
 ion\, and probability based inference.\n\n(The talk is based on joint work
  with Olli Saarela)\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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