Prediction rules for exchangeable sequences related to species sampling

Prediction rules for exchangeable sequences related to species sampling

Report Number
520
Authors
Ben Hansen and Jim Pitman
Citation
Electronic Journal of Probability</em>, Vol. 5 (2000) Paper no. 2, pages 1-18
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.

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