A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices
A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices
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一种快速生成随机相关矩阵的 Metropolis-Hastings 方法
DOI：
10.1007/978-3-030-03493-1_13
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Larrañaga
中科院分区：
文献类型：
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作者：
Irene Córdoba;Gherardo Varando;C. Bielza;P. Larrañaga
我们提出了一种新的Metropolis-Hastings算法，从相关矩阵的空间均匀采样。现有的方法都是基于相关矩阵的复杂表示或复杂参数化，而本文的方法基于正定矩阵的Cholesky分解和Markov链Monte Carlo理论，具有直观、简单的特点。我们进行了详细的收敛分析所产生的马尔可夫链，并显示它如何从快速收敛，理论和经验。此外，在数值实验中，我们的算法被证明是显着快于目前的替代方法，由于其简单而有原则的方法。
We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.