Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm
Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm
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DOI：
10.1016/j.csda.2011.11.020
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发表时间：
2012-06-01
影响因子：
1.8
通讯作者：
Mira, A.
中科院分区：
文献类型：
--
作者：
Rigat, F.;Mira, A.
提出了一种新型的相互作用马尔可夫链蒙特卡罗（MCMC）算法，即并行分层采样器（PHS），并对其混合性能进行了评价。小灵通算法是模块化的MCMC采样器，旨在为多模态和重尾后验分布产生可靠的估计。因此，小灵通旨在使从事广泛应用的统计学家受益，他们更专注于定义和完善模型，而不是构建复杂的抽样策略。在Metropolis-Hastings链内更新的情况下，证明了一种普通小灵通算法的收敛性。在多元高斯密度的多模态混合和“香蕉形”重尾多元分布情况下，将该PHS核与优化的单链和多链MCMC算法的精度进行了比较。这些例子表明，小灵通可以大大提高MCMC估计器的精度，而不是标准采样器。然后将小灵通应用于两种实际复杂的贝叶斯模型不确定性情景。首先，小灵通用于选择高斯线性回归模型中存在高共线性的低数量有意义的预测因子。其次，PHS近似的生存树后验概率表明，诊断时肝转移的数量和大小可以预测结直肠癌患者生存分布的实质性差异。(C) 2011 Elsevier B.V.版权所有
A novel class of interacting Markov chain Monte Carlo (MCMC) algorithms, hereby referred to as the Parallel Hierarchical Sampler (PHS), is developed and its mixing properties are assessed. PHS algorithms are modular MCMC samplers designed to produce reliable estimates for multi-modal and heavy-tailed posterior distributions. As such, PHS aims at benefitting statisticians whom, working on a wide spectrum of applications, are more focused on defining and refining models than constructing sophisticated sampling strategies. Convergence of a vanilla PHS algorithm is proved for the case of Metropolis-Hastings within-chain updates. The accuracy of this PHS kernel is compared with that of optimized single-chain and multiple-chain MCMC algorithms for multimodal mixtures of multivariate Gaussian densities and for 'banana-shaped' heavy-tailed multivariate distributions. These examples show that PHS can yield a dramatic improvement in the precision of MCMC estimators over standard samplers. PHS is then applied to two realistically complex Bayesian model uncertainty scenarios. First, PHS is used to select a low number of meaningful predictors for a Gaussian linear regression model in the presence of high collinearity. Second, the posterior probability of survival trees approximated by PHS indicates that the number and size of liver metastases at the time of diagnosis are predictive of substantial differences in the survival distributions of colorectal cancer patients. (C) 2011 Elsevier B.V. All rights reserved.