Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or smoothness. From a Bayesian perspective, these structural assumptions should be incorporated into an analysis through the prior distribution. In this work, we introduce a general approach to constructing prior distributions for structured semi-orthogonal matrices that leads to tractable posterior inference via parameter-expanded Markov chain Monte Carlo. We draw on recent results from random matrix theory to establish a theoretical basis for the proposed approach. We then introduce specific prior distributions for incorporating sparsity or smoothness and illustrate their use through applications to biological and oceanographic data.

翻译：多元数据的统计模型通常包含一个半正交矩阵参数。在许多应用中，有理由预期该半正交矩阵参数满足稀疏性或平滑性等结构假设。从贝叶斯视角来看，这些结构假设应通过先验分布融入分析过程。本研究提出一种构建结构化半正交矩阵先验分布的通用方法，该方法通过参数扩展的马尔可夫链蒙特卡罗方法实现可处理的后验推断。我们借鉴随机矩阵理论的最新成果，为所提方法建立理论基础。随后针对稀疏性与平滑性约束分别引入具体的先验分布，并通过生物学和海洋学数据的应用案例进行演示。