Prediction rules for exchangeable sequences related to species sampling
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 jth distinct value observed so far with probability pj,n, for j=1,2,... , and otherwise is a new value with distribution [nu] for some probability measure [nu] on S with no atoms. Then the pj,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 pj,n and in terms of their de Finetti representations.
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Volume (Year): 46 (2000)
Issue (Month): 3 (February)
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