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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Professor Cheng Cheng                             April 27, 2000
Department of Mathematical Sciences               304 Whitehead Hall
The Johns Hopkins University                      Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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                  TEST OF COMPLETE RANDOMNESS AND
           EXTRACTION OF CLUSTERS ON A HOMOGENEOUS SPACE

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                             ABSTRACT

Roughly speaking, as far as proability distributions are concerned, a
"homgeneous space" is a topological space on which the uniform distribution
can be properly defined.  Intervals, squares, cubes, and spheres are examples
of homogeneous spaces.  This talk will present a simulation-based statistical
test of complete randomness defined in terms of certain point processes on a
homogeneous space.  A Monte Carlo power study of testing complete randomness
on the unit sphere and open questions will be discussed.  Upon rejecting the
complete randomness null hypothesis, it is natural to further investigate
which observed points resulted in the rejection.  This leads to the cluster
extraction problem.  An algorithm for extracting clusters from the observed
points (data), along with an index measuring the "tightness" of the
clusters, will be presented.

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