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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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\begin{center}
  4:15 p.m., Tuesday, December 6, 2005\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{Herbie Lee} \\
  Department of Applied Math and Statistics\\
  University of California, Santa Cruz \\
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  \textbf{Adaptive Parameter Space Exploration and Nonstationary Modeling Using
  Gaussian Process Trees}
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\noindent

This work on adaptive non-stationary modeling was motivated by a
problem in aeronautical computer modeling.  Typically, a complete grid
of input parameter configurations for computer simulations is needed
to obtain even qualitative understanding of the simulation output. For
large scale simulations, such sweeps can be prohibitively expensive.
Thus there is a need for computationally inexpensive surrogate models
that can be used in place of simulation to adaptively select new
settings of input parameters and map the response with far fewer
simulation runs. We provide a general methodology for modeling and
adaptive sampling to greatly speed up parameter sweeps. Binary trees
are used to recursively partition the input space, and Gaussian
process models are fit within each partition. Trees facilitate
non-stationarity and a Bayesian interpretation provides a measure of
uncertainty in the sample space which can be used to guide future
sampling. These methods are illustrated on several examples, including
the motivating example involving computational fluid dynamics
simulation of a NASA reentry vehicle.




\noindent

This is joint work with Robert Gramacy and William Macready.



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