Object Oriented Data Analysis
Statistics 322
Fall Semester 2005
J. S. Marron
Department of Statistics and Operations Research
Tuesday - Thursday 12:30 - 1:45
Smith 107
Object Oriented Data Analysis is the statistical
analysis of populations of complex objects. In the special
case of Functional Data Analysis, these data objects are
curves, where standard Euclidean approaches, such as
principal components analysis, have been very successful.
Recent developments in medical image analysis motivate
the statistical analysis of populations of more complex data
objects which are elements of mildly non-Euclidean spaces,
such as Lie Groups and Symmetric Spaces, or of strongly
non-Euclidean spaces, such as spaces of tree-structured
data objects. These new contexts for Object Oriented Data
Analysis create several potentially large new interfaces
between mathematics and statistics. Even in situations
where Euclidean analysis makes sense, there are statistical
challenges because of the High Dimension Low Sample Size
problem, which motivates a new type of asymptotics leading
to non-standard mathematical statistics.
Prerequisite is some type of course experience with notions
of probability, expectation, variance, covariance, and the
multivariate normal distribution, e.g. as in Stat 164 (but
there are a number of other courses that will work as
well). Most fundamental statistical concepts that are
needed (e.g. Principal Component Analysis) will be
developed during the course.
Course grading will be done on the basis of student
presentations. The presentation will be either about the
student's own related work (rather broadly defined), or
else about a recent paper in the area.
Enrollment is encouraged, but auditors are also welcome.