Dirichlet过程的回顾Markov链Monte Carlo方法 层次模型

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摘要翻译：
Dirichlet过程分层模型的推理通常使用Markov链Monte Carlo方法，这些方法可以大致分为边缘方法和条件方法。前者利用Gibbs采样器从剩余变量的边缘分布中解析地集成出分层模型的无穷维分量和样本。条件法归入Dirichlet过程，并将其更新为Gibbs采样器的一个组成部分。由于这需要无限维过程的估算，条件方法的实现依赖于有限近似。在本文中，我们通过设计两个新的马尔可夫链蒙特卡罗算法来避免这种近似，这些算法是从感兴趣量的精确后验分布中采样的。采用回溯抽样的新技术避免了这种近似。我们还展示了算法如何从Dirichlet过程的泛函中获得样本。对边缘方法和条件方法进行了比较，并对非共轭模型、不同的数据集和先验规范进行了详细的仿真研究。
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英文标题：
《Retrospective Markov chain Monte Carlo methods for Dirichlet process
  hierarchical model》
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作者：
Omiros Papaspiliopoulos and Gareth Roberts
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
--

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英文摘要：
  Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorised 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.
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PDF链接：
https://arxiv.org/pdf/710.4228

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关键词：Monte Carlo Dirichlet Markov Carlo Mark 剩余 marginal using 边缘 Gibbs