Optimizing random scan Gibbs samplers
Optimizing random scan Gibbs samplers
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DOI：
10.1016/j.jmva.2006.05.008
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发表时间：
2006-11-01
影响因子：
1.6
通讯作者：
Casella, George
中科院分区：
文献类型：
--
作者：
Levine, Richard A.;Casella, George
吉布斯采样器是一种流行的马尔可夫链蒙特卡罗程序，用于从分布中生成随机变量，否则很难采样。许多实现可用于运行吉布斯采样器，其顺序不同，吉布斯采样器使用的完整条件分布被循环或访问。一个常见的，实际上是原始的实现是随机扫描策略，其中完整的条件分布在每次迭代中以随机选择的顺序更新。在本文中，我们介绍了一个随机扫描吉布斯采样器，自适应更新的选择概率或“学习”从所有以前的随机变量生成的吉布斯采样。在这个过程中，我们概述了一些变化的随机扫描吉布斯采样器，允许从业者许多选择设置的选择概率和证明收敛的诱导（马尔可夫）链的平稳分布的利益。虽然我们强调用户选择和规范这些随机扫描算法的灵活性，我们提出了一个极大极小随机扫描，通过决策理论的考虑，确定选择概率的精度估计的兴趣。我们说明和应用的结果，通过使用自适应随机扫描吉布斯采样器开发的样本从多变量高斯目标分布，自动采样器的后验模拟下的Dirichlet过程混合模型，并适合混合分布。(C)2006年爱思唯尔公司All rights reserved.
The Gibbs sampler is a popular Markov chain Monte Carlo routine for generating random variates from distributions otherwise difficult to sample. A number of implementations are available for running a Gibbs sampler varying in the order through which the full conditional distributions used by the Gibbs sampler are cycled or visited. A common, and in fact the original, implementation is the random scan strategy, whereby the full conditional distributions are updated in a randomly selected order each iteration. In this paper, we introduce a random scan Gibbs sampler which adaptively updates the selection probabilities or "learns" from all previous random variates generated during the Gibbs sampling. In the process, we outline a number of variations on the random scan Gibbs sampler which allows the practitioner many choices for setting the selection probabilities and prove convergence of the induced (Markov) chain to the stationary distribution of interest. Though we emphasize flexibility in user choice and specification of these random scan algorithms, we present a minimax random scan which determines the selection probabilities through decision theoretic considerations on the precision of estimators of interest. We illustrate and apply the results presented by using the adaptive random scan Gibbs sampler developed to sample from multivariate Gaussian target distributions, to automate samplers for posterior simulation under Dirichlet process mixture models, and to fit mixtures of distributions. (C) 2006 Elsevier Inc. All rights reserved.