Title: Prediction rules for exchangeable sequences related to species sampling
Author: Ben Hansen and Jim Pitman
Date: May 1998 
Abstract:
Suppose an exchangable sequence with values in a nice measurable space $S$
admits a prediction rule of the following form: given the first $n$ terms of
the sequence, the next term equals the $j$th distinct value observed so far
with probability $p_{j,n}$, for $j = 1,2, \ldots$, and otherwise is a new
value with distribution $\nu$ for some probability measure $\nu$ on $S$ with
no atoms. Then the $p_{j,n}$ depend only on the partitition of the first $n$
integers induced by the first $n$ values of the sequence. All possible
distributions for such an exchangeable sequence are characterized in terms of
constraints on the $p_{j,n}$ and in terms of their de Finetti representations.