Exchangeable and partially exchangeable random partitions
نویسنده
چکیده
Call a random partition of the positive integers partially exchangeable if for each finite sequence of positive integers n l , . . . , nk, the probability that the partition breaks the first nl + . . . § nk integers into k particular classes, of sizes nl . . . . , nk in order of their first elements, has the same value p(na . . . . . nk) for every possible choice of classes subject to the sizes constraint. A random partition is exchangeable iff it is partially exchangeable for a symmetric function p(nl , . . , nk). A representation is given for partially exchangeable random partitions which provides a useful variation of Kingman 's representation in the exchangeable case. Results are illustrated by the twoparameter generalization of Ewens ' partition structure.
منابع مشابه
Partially Exchangeable Random Partitions
A random partition of the positive integers is called partially exchangeable if for each finite sequence of positive integers n,, ... , nk, the probability that the partition breaks the first n1 + + nk integers into k particular classes, of sizes nl,.. . ., nk in order of their first elements, has the same value p(nl,...,nk) for every possible choice of classes subject to the sizes constraint. ...
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