A hierarchical version of the de Finetti and Aldous-Hoover representations

被引：13

作者：

Austin, Tim ^{[1
]}

Panchenko, Dmitry ^{[2
]}

机构：

[1] NYU, Courant Inst, New York, NY USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2014年 / 159卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Exchangeability; Spin glasses;

D O I：

10.1007/s00440-013-0521-0

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.

引用

页码：809 / 823

页数：15

共 14 条

[1] REPRESENTATIONS FOR PARTIALLY EXCHANGEABLE ARRAYS OF RANDOM-VARIABLES [J].