On MCMC sampling in hierarchical longitudinal models
On MCMC sampling in hierarchical longitudinal models
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DOI：
10.1023/a:1008853808677
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发表时间：
1999-01-01
影响因子：
2.2
通讯作者：
Carlin, BP
中科院分区：
文献类型：
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作者：
Chib, S;Carlin, BP
马尔可夫链蒙特卡罗 (MCMC) 算法彻底改变了贝叶斯实践。然而，以最简单的形式（即一次更新一个参数），当应用于高维统计模型时，它们的收敛速度通常很慢。解决此问题的方法是将参数分组，然后使用 Gibbs 或 Metropolis-Hastings 步骤同时更新这些参数。在本文中，我们构建了几种（部分和完全阻塞）MCMC 算法，用于最小化由重要类别的纵向数据模型产生的 MCMC 样本中的自相关性。我们利用 Chib (1995) 在贝叶斯因子计算中使用的恒等式来展示一般线性混合模型中的参数如何在单个块中更新，从而提高收敛性并根据感兴趣的参数的后验生成基本上独立的绘图。我们还研究了非高斯混合模型以及一类二元响应数据纵向模型中的阻塞值。我们通过三个真实数据示例详细说明了这些方法。
Markov chain Monte Carlo (MCMC) algorithms have revolutionized Bayesian practice. In their simplest form (i.e., when parameters are updated one at a time) they are, however, often slow to converge when applied to high-dimensional statistical models. A remedy for this problem is to block the parameters into groups, which are then updated simultaneously using either a Gibbs or Metropolis-Hastings step. In this paper we construct several (partially and fully blocked) MCMC algorithms for minimizing the autocorrelation in MCMC samples arising from important classes of longitudinal data models. We exploit an identity used by Chib (1995) in the context of Bayes factor computation to show how the parameters in a general linear mixed model may be updated in a single block, improving convergence and producing essentially independent draws from the posterior of the parameters of interest. We also investigate the value of blocking in non-Gaussian mixed models, as well as in a class of binary response data longitudinal models. We illustrate the approaches in detail with three real-data examples.