Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block structural learning, under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single link but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional independence structure. Since the elements of a B-Spline basis have compact support, the independence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.

翻译：在高斯图模型框架下，本文引入了一种关于底层图的先验分布，以诱导图邻接矩阵的块结构，并学习固定变量组之间的关系。针对块结构学习，基于共轭G-Wishart先验，提出了一种名为双可逆跳转马尔可夫链蒙特卡洛的新型采样策略。该算法不仅能够增加或删除单个链接，还能对整个边组进行操作。随后，该方法被应用于平滑函数型数据。通过在基展开系数上建立图模型，改进了经典平滑过程，从而估计其条件独立结构。由于B样条基的元素具有紧支撑性，该独立结构反映在定义明确的空间域部分上。利用函数域的已知划分，可研究化合物内各物质之间的关系。