Prediction rules for exchangeable sequences related to species sampling

Ben Hansen and Jim Pitman

Statistics & Probability Letters, 2000, vol. 46, issue 3, 251-256

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 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.

Keywords: Exchangeable; sequence; Prediction; rule; Species; sampling (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (8)

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