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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem
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Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem

机译：经验贝叶斯分层模型，用于正则化矩阵高斯Procrustes问题中的最大似然估计

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摘要

Procrustes analysis involves finding the optimal superposition of two or more "forms" via rotations, translations, and scalings. Procrustes problems arise in a wide range of scientific disciplines, especially when the geometrical shapes of objects are compared, contrasted, and analyzed. Classically, the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms. Despite its widespread use, the ordinary unweighted least-squares (LS) criterion can give erroneous solutions when the errors have heterogeneous variances (heteroscedasticity) or the errors are correlated, both common occurrences with real data. In contrast, maximum likelihood (ML) estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation. Here we provide a complete solution to the nonisotropic ML Procrustes problem assuming a matrix Gaussian distribution with factored covariances. Our analysis generalizes, simplifies, and extends results from previous discussions of the ML Procrustes problem. An iterative algorithm is presented for the simultaneous, numerical determination of the ML solutions.
机译：前驱力分析涉及通过旋转，平移和缩放找到两个或多个“形式”的最佳叠加。在广泛的科学学科中，特别是在比较，对比和分析对象的几何形状时，会出现壳体问题。传统上，通过最小化表单中相应点之间的平方距离之和来找到最佳变换。尽管已被广泛使用，但当错误具有异质方差（异方差）或错误相关时，普通的非加权最小二乘（LS）准则仍会给出错误的解决方案，这两种情况都与真实数据有关。相反，在存在异方差性和相关性的情况下，最大似然（ML）估计可以提供准确且一致的统计估计。在这里，我们提供了一个非同质的ML Procrustes问题的完整解决方案，假设矩阵的高斯分布具有因子协方差。我们的分析概括，简化和扩展了ML Procrustes问题先前讨论的结果。提出了一种迭代算法，用于同时确定ML解的数值。

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