Generalized weighted Chinese restaurant processes for species sampling mixture models
Generalized weighted Chinese restaurant processes for species sampling mixture models
复制标题
物种抽样混合模型的广义加权中餐馆流程
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Lancelot F. James
中科院分区：
文献类型：
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作者：
H. Ishwaran;Lancelot F. James
引入物种抽样混合模型类，将基于Dirichlet过程的半参数模型推广到基于一般物种抽样先验类或等价于所有可交换分布类的模型.利用Fubini演算结合皮特曼（1995，1996），我们得到了后验分布的特征，推广了Lo（1984）关于Dirichlet过程的结果。这些结果提供了一个更好的理解模型，并具有理论和实际应用。为了便于使用我们的模型，我们推广了Brunner，Chan，James和Lo（2001）的工作，通过扩展他们的加权中国餐馆（WCR）Monte Carlo程序，一个独立同分布。基于Dirichlet过程，将序贯重要性抽样（SIS）方法应用于物种抽样混合模型中平均泛函及其后验律的逼近.我们还讨论了塌陷Gibbs抽样、Polya瓮Gibbs抽样和一个Polya瓮SIS方案。我们的框架允许众多的应用，包括乘法计数过程模型的加权伽玛过程，以及非参数和半参数的层次模型的基础上的Dirichlet过程，其两个参数的扩展，Pitman-Yor过程和有限维Dirichlet先验。
The class of species sampling mixture models is introduced as an exten- sion of semiparametric models based on the Dirichlet process to models based on the general class of species sampling priors, or equivalently the class of all exchangeable urn distributions. Using Fubini calculus in conjunction with Pitman (1995, 1996), we derive characterizations of the posterior distribution in terms of a posterior par- tition distribution that extend the results of Lo (1984) for the Dirichlet process. These results provide a better understanding of models and have both theoretical and practical applications. To facilitate the use of our models we generalize the work in Brunner, Chan, James and Lo (2001) by extending their weighted Chinese restaurant (WCR) Monte Carlo procedure, an i.i.d. sequential importance sampling (SIS) procedure for approximating posterior mean functionals based on the Dirich- let process, to the case of approximation of mean functionals and additionally their posterior laws in species sampling mixture models. We also discuss collapsed Gibbs sampling, Polya urn Gibbs sampling and a Polya urn SIS scheme. Our framework allows for numerous applications, including multiplicative counting process models subject to weighted gamma processes, as well as nonparametric and semiparamet- ric hierarchical models based on the Dirichlet process, its two-parameter extension, the Pitman-Yor process and finite dimensional Dirichlet priors.