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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  %% Time of talk, Weekday, Date of talk\\
  %% Example: 4:15 p.m., Tuesday, November 20th, 2007\\
  4:15 p.m., Tuesday, February 12th, 2008\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Ethan Anderes} \\
  UC Berkeley
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  \subsection*{Two Topics in Spatial Statistics: Estimating Cloud Height from 
Multi-Angle Satellite Imagery and Deformed Random Fields}
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\noindent
In this talk I will present two recent research projects, both relating to 
random fields and spatial statistics. Although one project is applied and 
one is theoretical, both consider the scenario where one observes a dense 
realization of a two-dimensional random field without replicates.

The first part of the talk will present a recent collaboration with Bin Yu 
(UC Berkeley) and the MISR team at the Jet Propulsion Laboratory in which 
we developed a new stereo matching algorithm for cloud height estimation 
using multi-angle cameras provided by the MISR instrument on the Terra 
satellite.
Clouds play an integral role in determining the Earth's energy budget. As 
a result,  monitoring and characterizing the
distribution of clouds is essential  in global climate studies. By viewing 
the multi-angle cloud images as discrete sub-samples of a continuous 
random  field, one can view  cloud-top height estimation as a statistical 
parameter estimation problem.
This paradigm sheds fresh light on the feature matching problem and 
provides a framework for developing computational techniques and 
incorporating technical details of the MISR instrument for improving 
height estimates.

The second part of the talk will present a new fixed domain asymptotic 
result, in collaboration with Sourav Chatterjee (UC Berkeley), for 
estimating the deformation of an isotropic Gaussian random field.  The 
estimates are constructed using directional quadratic variations to 
estimate components of a singular value decomposition of the Jacobian. The 
remaining estimable components  are recovered by a projection onto the 
Bergman space of holomorphic maps. If time permits we will discuss further 
details of the proof and future applications.
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