Post-processing for Bayesian analysis of reduced rank regression models with orthonormality restrictions

IF 1.4 4区 数学 Q2 STATISTICS & PROBABILITY
Christian Aßmann, Jens Boysen-Hogrefe, Markus Pape
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引用次数: 0

Abstract

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.

Abstract Image

对具有正交限制的缩减秩回归模型进行贝叶斯分析的后处理
正交性约束是还原秩模型中常见的约束条件。它们意味着矩阵变量参数是以正交列向量的形式给出的。然而,这些正交性限制并不能识别所有参数。对于这种设置,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。这就扩展了贝叶斯推理在缩小秩回归模型中的应用,其参数空间的一部分被限制在 Stiefel 流形中。除了推理,我们还从后验预测评估的角度讨论了模型选择。我们通过模拟研究和经验应用来说明所提出的方法。
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来源期刊
Asta-Advances in Statistical Analysis
Asta-Advances in Statistical Analysis 数学-统计学与概率论
CiteScore
2.20
自引率
14.30%
发文量
39
审稿时长
>12 weeks
期刊介绍: AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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