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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, April 23, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Marc Coram}
\centerline{\sl Department of Statistics}
\centerline{\sl Stanford University}
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\centerline{\bf Nonparametric Bayesian Classification}
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A Bayesian approach to the classification problem is proposed in which
random partitions play a central role. It is argued that the
partitioning approach has the capacity to take advantage of a variety
of large-scale spatial structures, if they are present in the
unknown regression function $f_0$. An idealized one-dimensional
problem is considered in detail. The proposed nonparametric prior is
found to provide a consistent estimate of the regression function in
the $\L^p$ topology, for any $1 \leq p < \infty$, and for arbitrary
measurable $f_0:[0,1] \rightarrow [0,1]$. An MCMC implementation is
outlined and simulation experiments are conducted to show that the
proposed estimate compares favorably with CART and bagged CART
estimates. A generalized prior is discussed which employs a random
Voronoi partition of the covariate-space. The resulting estimate
displays promise on a two-dimensional problem, and extends with a
minimum of additional computational effort to arbitrary metric spaces.

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