Gibbs sampling methods for stick-breaking priors
Gibbs sampling methods for stick-breaking priors
复制标题
DOI：
10.1198/016214501750332758
复制
发表时间：
2001-03-01
影响因子：
3.7
通讯作者：
James, LF
中科院分区：
文献类型：
--
作者：
Ishwaran, H;James, LF
可以使用一系列独立的 beta 随机变量来构造一类丰富而灵活的随机概率度量，我们称之为断棍钳。具有这种特征的随机度量的示例包括狄利克雷过程、其双参数扩展、双参数泊松-狄利克雷过程、有限维狄利克雷先验和 beta 双参数过程。断棍先验的丰富性质为贝叶斯学派提供了用于非参数问题的一类有用的先验，而每个先验中使用的类似构造可用于开发用于拟合它们的通用计算程序。在本文中，我们提出了两种通用类型的吉布斯采样器，可用于基于破棒先验来点亮贝叶斯分层模型的后验。第一种类型的吉布斯采样器，称为 Polya urn Gibbs 采样器，是当前用于狄利克雷过程计算的广泛使用的吉布斯采样方法的通用版本。该方法适用于具有已知波利亚瓮特征的破棍先验，即具有明确且简单的预测规则的先验。我们的第二种方法是阻塞吉布斯采样器，它基于一种完全不同的方法，该方法通过直接从随机测量的后验中采样值来工作。阻塞吉布斯采样器可以被视为一种更通用的方法，因为它不需要显式的预测规则即可工作。我们发现阻塞式吉布斯避免了波利亚瓮方法的一些限制，并且对于非专家来说应该更容易使用。
A rich and flexible class of random probability measures, which we call stick-breaking pliers, can be constructed using a sequence of independent beta random variables. Examples of random measures that have this characterization include the Dirichlet process, its two-parameter extension, the two-parameter Poisson-Dirichlet process, finite dimensional Dirichlet priors, and beta two-parameter processes. The rich nature of stick-breaking priors offers Bayesians a useful class of priors for nonparametric problems, while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them. In this article we present two general types of Gibbs samplers that can be used to lit posteriors of Bayesian hierarchical models based on stick-breaking priors. The first type of Gibbs sampler, referred to as a Polya urn Gibbs sampler, is a generalized version of a widely used Gibbs sampling method currently employed for Dirichlet process computing. This method applies to stick-breaking priors with a known Polya urn characterization, that is, priors with an explicit and simple prediction rule. Our second method, the blocked Gibbs sampler, is based on an entirely different approach that works by directly sampling values from the posterior of the random measure. The blocked Gibbs sampler can be viewed as a more general approach because it works without requiring an explicit prediction rule. We find that the blocked Gibbs avoids some of the limitations seen with the Polya urn approach and should be simpler for nonexperts to use.