Sampling decomposable graphs using a Markov chain on junction trees
Sampling decomposable graphs using a Markov chain on junction trees
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DOI：
10.1093/biomet/ass052
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发表时间：
2013-03-01
期刊：
影响因子：
2.7
通讯作者：
Thomas, Alun
中科院分区：
文献类型：
--
作者：
Green, Peter J.;Thomas, Alun
在无向图模型中，用于模型确定的完全贝叶斯计算推理目前仅限于可分解图或其他特殊情况，除了小规模问题，比如多达15个变量。在本文中，我们开发了新的，更有效的方法，这样的推理，通过两个贡献的计算几何的可分解图。其中第一个提供了充分条件，在此条件下，可以完全连接两个不连通的完全顶点子集，或者执行相反的过程，但保持图的可分解性。第二个是一种新的马尔可夫链蒙特卡罗采样器，用于可分解图上的任意正分布，以代表图的联合树作为其状态变量。所得到的方法与三个模型上的数值实验说明。
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs or other special cases, except for small-scale problems, say up to 15 variables. In this paper we develop new, more efficient methodology for such inference, by making two contributions to the computational geometry of decomposable graphs. The first of these provides sufficient conditions under which it is possible to completely connect two disconnected complete subsets of vertices, or perform the reverse procedure, yet maintain decomposability of the graph. The second is a new Markov chainMonte Carlo sampler for arbitrary positive distributions on decomposable graphs, taking a junction tree representing the graph as its state variable. The resulting methodology is illustrated with numerical experiments on three models.