Decomposable graphical Gaussian model determination
Decomposable graphical Gaussian model determination
复制标题
DOI：
10.1093/biomet/86.4.785
复制
发表时间：
1999-12-01
期刊：
影响因子：
2.7
通讯作者：
Green, PJ
中科院分区：
文献类型：
--
作者：
Giudici, P;Green, PJ
提出了一种在可分解的图形高斯模型中确定贝叶斯模型的方法。为了达到这一目的，我们考虑了每个给定图的浓度矩阵上的超逆Wishart先验分布。为了确保模型之间的兼容性，这样的先验分布是通过对完整图上的先验条件进行边际化来获得的。我们探索了后者的超参数的替代结构，以及它们对模型的影响。模型的确定通过实现可逆跳跃马尔可夫链蒙特卡罗采样器来实现。具体地说，我们提出的改变维度的移动涉及在图中添加或删除边。我们刻画了保持图的可分解性的移动集，给出了一种在每次扫描时保持图的连接树表示的快速算法。作为状态变量，我们使用不完全方差-协方差矩阵，它只包含逆的相应元素非零的元素。这使得所有计算都可以在集团级别上本地执行，这对于分析大型和复杂的数据集来说是一个明显的优势。最后，用人工数据集和真实数据集说明了该方法的统计和计算性能。
We propose a methodology for Bayesian model determination in decomposable graphical Gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility across models, such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. We explore alternative structures for the hyperparameters of the latter, and their consequences for the model. Model determination is carried out by implementing a reversible jump Markov chain Monte Carlo sampler. In particular, the dimension-changing move we propose involves adding or dropping an edge from the graph. We characterise the set of moves which preserve the decomposability of the graph, giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep. As state variable, we use the incomplete variance-covariance matrix, containing only the elements for which the corresponding element of the inverse is nonzero. This allows all computations to be performed locally, at the clique level, which is a clear advantage for the analysis of large and complex datasets. Finally, the statistical and computational performance of the procedure is illustrated by mean of both artificial and real datasets.