基于倾斜的随机概率测度共轭类及其后验分析
摘要
本文构造了一类随机概率测度，其基于对完全随机测度 (completely random measures) 的律进行指数倾斜和多项式倾斜操作。该类被证明在贝叶斯意义下是共轭的，因为它同时涵盖了先验和后验随机概率测度。此外，该构造统一包含了一些常见且广泛使用的随机概率测度，包括归一化完全随机测度 (normalized completely random measures) (James (Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics (2002) Preprint), Regazzini, Lijoi and Pr"{u}nster (Ann. Statist. 31 (2003) 560-585), Lijoi, Mena and Pr"{u}nster (J. Amer. Statist. Assoc. 100 (2005) 1278-1291)) 以及 Poisson-Dirichlet 过程 (Pitman and Yor (Ann. Probab. 25 (1997) 855-900), Ishwaran and James (J. Amer. Statist. Assoc. 96 (2001) 161-173), Pitman (In Science and Statistics: A Festschrift for Terry Speed (2003) 1-34 IMS))。我们描述了一种增强版的 Blackwell-MacQueen P\'{o}lya 瓮抽样方案 (Blackwell and MacQueen (Ann. Statist. 1 (1973) 353-355))，该方案简化了实现过程，并提供了一项模拟研究以近似划分大小的概率。
引用
@article{arxiv.1312.5137,
title = {A conjugate class of random probability measures based on tilting and with its posterior analysis},
author = {John W. Lau},
journal= {arXiv preprint arXiv:1312.5137},
year = {2013}
}
备注
Published in at http://dx.doi.org/10.3150/12-BEJ467 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)