In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of parameters as a function of the dimension. We suggest an automatic approach to define a prior using a natural sequence of simpler models within the Penalized Complexity framework for the unknown parameters in these models. We illustrate this approach with three applications: a multivariate linear regression of four biomarkers, a multivariate disease mapping, and a multivariate longitudinal joint modelling. Each application underscores our method's intuitive appeal, signifying a substantial advancement toward a more cohesive and enlightening model that facilitates a meaningful interpretation of correlation matrices.

翻译：本文提出了一种构建具有用户定义图形结构的相关矩阵模型的新方法。该图形化结构使得相关矩阵具有可解释性，并避免了参数数量随维度呈二次增长。我们提出了一种自动化方法，在惩罚复杂度框架内，利用一系列自然简化的模型为这些模型中的未知参数定义先验分布。我们通过三个应用实例阐释了该方法：四项生物标志物的多元线性回归、多元疾病制图以及多元纵向联合建模。每个应用都凸显了我们方法的直观吸引力，标志着在构建更统一、更具启发性的模型方面取得了实质性进展，从而促进了对相关矩阵的有意义解释。