On block updating in Markov random field models for disease mapping. (REVISED, May 2001)
On block updating in Markov random field models for disease mapping. (REVISED, May 2001)
复制标题
用于疾病绘图的马尔可夫随机场模型的块更新。
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
H. Rue
中科院分区：
文献类型：
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作者：
L. Knorr‐Held;H. Rue
高斯马尔可夫随机场 (GMRF) 模型通常用于对疾病绘图应用中的空间相关性进行建模。对于 MCMC 的贝叶斯推理，到目前为止主要考虑的是单站点更新算法。然而，由于后验分布中参数的强烈依赖性，此类算法的收敛和混合特性可能非常糟糕。在本文中，我们提出了各种块采样算法以提高 MCMC 性能。该方法相当通用，允许非标准的完整条件，并且可以以模块化方式应用于大量不同的场景。为了便于说明，我们考虑三种不同的模型：用于单一疾病空间建模的两种公式（分别具有和不具有附加非结构化参数），以及用于两种疾病联合分析的一种公式。我们将所提出的算法应用于文献中已知的两个数据集。结果表明，如果参数和相应的超参数在一个大块中联合更新，可以获得最大的好处。在某些情况下，甚至可能需要更新一个块中的所有或几乎所有参数。使用高斯马尔可夫随机场快速采样方法，实现这种块算法非常容易（Rue，2000）。相比之下，基于单点更新的相对风险和相关量（例如超出相对风险的后验概率）的估计可能相当具有误导性，即使对于很长的运行也是如此。我们的结果可能与马尔可夫随机场分量的分层模型中的有效 MCMC 模拟具有更广泛的相关性。
Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely bad due to strong dependencies of parameters in the posterior distribution. In this paper, we propose various block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for non-standard full conditionals, and can be applied in a modular fashion in a large number of different scenarios. For illustration we consider three different models: two formulations for spatial modelling of a single disease (with and without additional unstructured parameters respectively), and one formulation for the joint analysis of two diseases. We apply the proposed algorithms to two datasets known from the literature. The results indicate that the largest benefits are obtained if parameters and the corresponding hyperparameter are updated jointly in one large block. In certain situations, even updating of all or nearly all parameters in one block may be necessary. Implementation of such block algorithms is surprisingly easy using methods for fast sampling of Gaussian Markov random fields (Rue, 2000). By comparison, estimates of the relative risk and related quantities, such as the posterior probability of an exceedence relative risk, based on single-site updating, can be rather misleading, even for very long runs. Our results may have wider relevance for efficient MCMC simulation in hierarchical models with Markov random field components.