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.