Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models
Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models
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DOI：
10.1093/biomet/asm086
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发表时间：
2008-03-01
期刊：
影响因子：
2.7
通讯作者：
Roberts, Gareth O.
中科院分区：
文献类型：
--
作者：
Papaspiliopoulos, Omiros;Roberts, Gareth O.
狄利克雷过程分层模型的推理通常使用马尔可夫链蒙特卡罗方法进行，其可以大致分为边际方法和条件方法。前者将层次模型的无穷维分量解析地整合出来，并使用吉布斯采样器从剩余变量的边缘分布中采样。条件方法估算狄利克雷过程，并将其更新为吉布斯采样器的一个组成部分。由于这需要一个无限维的过程，实施的条件方法依赖于有限的近似。在本文中，我们将展示如何避免这样的近似设计两种新的马尔可夫链蒙特卡罗算法的样本从精确的后验分布的数量感兴趣。通过回顾性抽样的新技术避免了近似值。我们还展示了如何从Dirichlet过程的泛函中获得样本的算法。边际和条件的方法进行了比较，并仔细的模拟研究，其中包括一个非共轭模型，不同的数据集和先验规范。
Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the Gibbs sampler. Conditional methods impute the Dirichlet process and update it as a component of the Gibbs sampler. Since this requires imputation of an infinite-dimensional process, implementation of the conditional method has relied on finite approximations. In this paper, we show how to avoid such approximations by designing two novel Markov chain Monte Carlo algorithms which sample from the exact posterior distribution of quantities of interest. The approximations are avoided by the new technique of retrospective sampling. We also show how the algorithms can obtain samples from functionals of the Dirichlet process. The marginal and the conditional methods are compared and a careful simulation study is included, which involves a non-conjugate model, different datasets and prior specifications.