Posterior Analysis for Normalized Random Measures with Independent Increments
Posterior Analysis for Normalized Random Measures with Independent Increments
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DOI：
10.1111/j.1467-9469.2008.00609.x
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发表时间：
2009-03-01
影响因子：
1
通讯作者：
Prunster, Igor
中科院分区：
文献类型：
--
作者：
James, Lancelot F.;Lijoi, Antonio;Prunster, Igor
贝叶斯非参数理论的主要研究领域之一是提出和研究推广Dirichlet过程的先验。在本文中，我们提供了一个全面的贝叶斯非参数分析的随机概率，这是通过归一化随机测量与独立增量（NRMI）。这些先验的特殊情况已经被证明是有用的统计应用，如混合模型和物种抽样问题。然而，为了充分利用这些先验知识，推导NRMI的后验分布是至关重要的：在这里，我们实现了这一目标，并确实提供了适合实际实施的明确和易于处理的表达式。NRMI的后验分布是一个特定潜变量分布的混合。通过推导相应的预测分布和对边际结构的深入研究，完成了分析。这些结果允许推导出一个广义的Blackwell-MacQueen抽样方案，然后将其调整为覆盖由一般NRMI驱动的混合模型。
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. In this paper, we provide a comprehensive Bayesian non-parametric analysis of random probabilities which are obtained by normalizing random measures with independent increments (NRMI). Special cases of these priors have already shown to be useful for statistical applications such as mixture models and species sampling problems. However, in order to fully exploit these priors, the derivation of the posterior distribution of NRMIs is crucial: here we achieve this goal and, indeed, provide explicit and tractable expressions suitable for practical implementation. The posterior distribution of an NRMI turns out to be a mixture with respect to the distribution of a specific latent variable. The analysis is completed by the derivation of the corresponding predictive distributions and by a thorough investigation of the marginal structure. These results allow to derive a generalized Blackwell-MacQueen sampling scheme, which is then adapted to cover also mixture models driven by general NRMIs.