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：本文提出了一种新方法，用于构建具有用户定义图形结构的相关矩阵模型。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，通过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。我们通过三个应用案例展示了该方法：四类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优势，标志着在构建更统一、更具启发性的模型方面取得了重要进展，从而促进了对相关矩阵的有意义解释。