Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior
Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior
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DOI：
10.1007/s11203-005-6071-z
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发表时间：
2005-12
影响因子：
0.8
通讯作者：
Antonio Lijoi;R. H. Mena;Igor Prünster
中科院分区：
文献类型：
--
作者：
Antonio Lijoi;R. H. Mena;Igor Prünster
本文考虑了Dirichlet过程的推广，它是通过适当地归一化具有递增的整数值尺度参数的叠加独立伽玛过程而得到的。提供了这种随机概率测度的综合处理。我们证明了有关其有限维分布，矩，预测分布和分布的平均值。大多数表达式给出了多个超几何函数，从而突出了贝叶斯Nonparametrics和特殊功能之间的相互作用。最后，应用合适的模拟算法以计算统计感兴趣的量。
This paper considers a generalization of the Dirichlet process which is obtained by suitably normalizing superposed independent gamma processes having increasing integer-valued scale parameter. A comprehensive treatment of this random probability measure is provided. We prove results concerning its finite-dimensional distributions, moments, predictive distributions and the distribution of its mean. Most expressions are given in terms of multiple hypergeometric functions, thus highlighting the interplay between Bayesian Nonparametrics and special functions. Finally, a suitable simulation algorithm is applied in order to compute quantities of statistical interest.