Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two components through a rotation. One component involves only the nuisance parameters, which can then be integrated out using a novel type of Gaussian approximation. We provide theory on approximation accuracy that holds for a broad class of forms of the nuisance component and priors. Applying our method to simulated and real data sets shows that it can outperform state-of-the-art posterior approximation approaches.

中文翻译：

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通过集成旋转高斯逼近用高维有害参数逼近后验

具有许多参数的高维数据的后验计算可能具有挑战性。本文重点介绍一种新方法，用于在存在高维或其他计算上具有挑战性的有害参数的情况下近似低维到中等维参数的后验分布。重点是回归模型，关键思想是通过旋转将可能性分成两个部分。一个组件仅涉及令人讨厌的参数，然后可以使用一种新型的高斯近似将其整合出来。我们提供了关于近似精度的理论，该理论适用于各种形式的滋扰成分和先验。将我们的方法应用于模拟和真实数据集表明，它可以优于最先进的后验近似方法。