Orthonormality constraints are common in reduced rank models. They imply that matrix-variate parameters are given as orthonormal column vectors. However, these orthonormality restrictions do not provide identification for all parameters. For this setup, we show how the remaining identification issue can be handled in a Bayesian analysis via post-processing the sampling output according to an appropriately specified loss function. This extends the possibilities for Bayesian inference in reduced rank regression models with a part of the parameter space restricted to the Stiefel manifold. Besides inference, we also discuss model selection in terms of posterior predictive assessment. We illustrate the proposed approach with a simulation study and an empirical application.

正交性约束在降阶模型中很常见。它们意味着矩阵变量参数以正交列向量的形式给出。然而，这些正交性限制并不能提供所有参数的识别。对于此设置，我们展示了如何通过根据适当指定的损失函数对采样输出进行后处理，在贝叶斯分析中处理剩余的识别问题。这扩展了降阶回归模型中贝叶斯推理的可能性，其中部分参数空间仅限于 Stiefel 流形。除了推理之外，我们还讨论后验预测评估方面的模型选择。我们通过模拟研究和实证应用来说明所提出的方法。