Exchangeable Gibbs partitions and Stirling triangles
نویسندگان
چکیده
منابع مشابه
Record indices and age-ordered frequencies in Exchangeable Gibbs Partitions
We consider a random partition Π of N = {1, 2, . . .} such that, for each n, its restriction Πn to [n] = {1, . . . , n} is given by an exchangeable Gibbs partition with parameters α, V for α ∈ (−∞, 1] and V = (Vn,k) defined recursively by setting V1,1 = 1 and Vn,k = (n− αk)Vn+1,k + Vn+1,k+1 k ≤ n = 1, 2, . . . (Gnedin and Pitman 2006). By ranking the blocks Πn1, . . . , Πnk of Πn by their age-o...
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SERGIO BACALLADO, STEFANO FAVARO and LORENZO TRIPPA Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA. E-mail: [email protected] Department of Economics and Statistics, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy. E-mail: [email protected] Harvard School of Public Health and Dana-Faber Cancer Institute, 450 Brooklin...
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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...
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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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Under a partition of the set N we shall mean a sequence (b1, b2, . . .) of subsets of N such that (i) the sets bj are disjoint, (ii) ∪jbj = N, (iii) if bk = ∅ then also bk+1 = ∅ and (iv) if bk+1 6= ∅ then min bk < min bk+1. Condition (iv) says that the sequence of minimal elements of the blocks is increasing. One can think of partition as a mapping which sends a generic element j ∈ N to one of ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2006
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-006-0335-z