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：本文提出了一种新颖的建模方法，用于构建具有用户定义图形结构的相关矩阵。该图形结构使相关矩阵具备可解释性，并避免了参数随维度呈二次增长的缺陷。我们建议采用一种自动化方法，通过在惩罚复杂性框架内使用一系列天然递进的简化模型来定义这些模型中未知参数的先验分布。该方法在三个应用中得到了验证：四类生物标志物的多元线性回归、多元疾病映射以及多元纵向联合建模。每个应用均凸显了该方法的直观优势，标志着在建立更统一且更具启发性的模型方面取得了实质性进展，从而促进对相关矩阵进行有意义的解释。