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"Infinite Exchangeability and Random Set Partitions"
Jie Yang
Department of Statistics, University of Chicago
WEDNESDAY, November 17, 2004, 4:15pm
Eckhart Hall, Room 110, 5734 S. University Avenue
This talk aims to introduce a Bayesian idea on multiple comparisons or simultaneous inference.
Instead of constructing statistics for comparing variety means in pairs, we start with an
infinitely exchangeable Gaussian prior for the variety effects such that each pair of varieties is
equal with positive prior probability. Consistency conditions on joint exchangeable priors
involving set partitions are discussed. The marginal posterior distribution on variety partitions
is studied in an effort to interpret the real relations among them. The comparison with classical
results is also given, as well as the marginal posterior distribution on group means involving
set partitions. Finally, some applications to cluster analysis are discussed.