Abstract A nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor is consistent in the sense that it tends to infinity under the alternative, and zero under the null. A p -value is then obtained through a permutation test based on the observed Bayes factor. Through a series of simulation studies, the performance of the proposed approach is examined and compared to several existing approaches based on the power of the test as well as the observed Bayes factor. Lastly, the proposed method is applied to a set of real data in ecology.

中文翻译：

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随机向量之间独立性的贝叶斯非参数检验

摘要 提出了一种用于检验连续随机变量组间独立性的非参数方法。以高斯为中心的多元有限 Polya 树先验用于对潜在概率分布进行建模。综合随机概率度量，推导出一个易于处理的经验贝叶斯因子并将其用作检验统计量。贝叶斯因子是一致的，因为它在替代项下趋于无穷大，而在零项下趋向于零。然后通过基于观察到的贝叶斯因子的置换测试获得 p 值。通过一系列模拟研究，基于测试的功效以及观察到的贝叶斯因子，检查了所提出方法的性能并与几种现有方法进行了比较。最后，将所提出的方法应用于生态学中的一组真实数据。