We describe the implementation of the Giudici-Green Metropolis sampling method for decomposable graphs using a variety of structures to represent the graph. These comprise the graph itself, the Junction tree, the Almond tree and the Ibarra clique-separator graph. For each structure, we describe the process for ascertaining whether adding or deleting a specific edge results in a new graph that is also decomposable, and the updates that need to be made to the structure if the edge perturbation is made. For the Almond tree and Ibarra graph these procedures are novel. We find that using the graph itself is generally at least competitive in terms of computational efficiency for a variety of graph distributions, but note that the other structures may allow and suggest samplers using different perturbations with lower rejection rates and/or better mixing properties. The sampler has applications in estimating graphical models for systems of multivariate Gaussian or Multinomial variables.

翻译：本文描述了使用多种结构表示可分解图时Giudici-Green Metropolis采样方法的实现。这些结构包括图本身、联结树、杏仁树和Ibarra团-分隔图。针对每种结构，我们阐述了判定添加或删除特定边是否生成新的可分解图的过程，以及实施边扰动时需对该结构进行的更新。其中杏仁树和Ibarra图对应的程序为全新设计。研究发现，对于多种图分布，使用图本身在计算效率上通常至少具有竞争力，但其他结构可能允许并启发采用不同扰动的采样器，从而实现更低的拒绝率和/或更好的混合性质。该采样器可应用于多元高斯或多项变量系统的图模型估计。