A popular class of priors for symmetric positive-definite matrices assumes independent entries and adds a truncation to ensure positive-definiteness. While conceptually simple and often computationally convenient, unless done carefully this truncation can have unintended effects. If the truncated prior or its margins are significantly different from their untruncated counterpart, then its interpretability may suffer, its shrinkage properties become harder to characterise, and posterior inference may be affected in unanticipated ways. We investigate the effect of the truncation both for dense and sparse matrices, and show how to set prior parameters such as the variance of off-diagonal entries such that said effect is mitigated as the matrix dimension grows. We pay particular attention to sparse inference where, unless prior parameters are set carefully, the truncated prior and hence its corresponding posterior assign systematically higher mass to sparser structures than the untruncated prior.

翻译：一类针对对称正定矩阵的流行先验假设矩阵元素独立分布，并通过截断处理确保正定性。虽然此类方法概念简单且常具计算便利性，但若操作不当，截断处理可能产生非预期影响。当截断先验或其边缘分布与未截断版本存在显著差异时，其可解释性可能受损，压缩特性更难刻画，后验推断也可能受到难以预料的干扰。本文研究了稠密矩阵与稀疏矩阵中截断效应的影响，并展示了如何设置先验参数（如非对角元方差），使得该效应随矩阵维度增大而削弱。我们特别关注稀疏推断场景：若未谨慎设置先验参数，截断先验及其对应后验相较于未截断先验，会对更稀疏结构赋予系统性更高权重。