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Record Indices and Age-Ordered Frequencies in Exchangeable Gibbs Partitions


 
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1. Title Title of document Record Indices and Age-Ordered Frequencies in Exchangeable Gibbs Partitions
 
2. Creator Author's name, affiliation, country Robert C. Griffiths; University of Oxford
 
2. Creator Author's name, affiliation, country Dario Spano; University of Oxford
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Exchangeable Gibbs Partitions, GEM distribution,Age-ordered frequencies, Beta-Stacy distribution, Neutral distributions, Record indices
 
3. Subject Subject classification Primary 60C05, 60G57, 62E10
 
4. Description Abstract The frequencies of an exchangeable Gibbs random partition of the integers (Gnedin and Pitman 2005) are considered in their age-order, i.e. their size-biased order. We study their dependence on the sequence of record indices (i.e. the least elements) of the blocks of the partition. In particular we show that, conditionally on the record indices, the distribution of the age-ordered frequencies has a left-neutral stick-breaking structure. Such a property in fact characterizes the Gibbs family among all exchangeable partitions and leads to further interesting results on: (i) the conditional Mellin transform of the $k$-th oldest frequency given the $k$-th record index, and (ii) the conditional distribution of the first $k$ normalized frequencies, given their sum and the $k$-th record index; the latter turns out to be a mixture of Dirichlet distributions. Many of the mentioned representations are extensions of Griffiths and Lessard (2005) results on Ewens' partitions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC grant GR/T21783/01
 
7. Date (YYYY-MM-DD) 2007-08-25
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/434
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-434
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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