Abstract The correlation coefficient is a commonly used criterion to measure the strength of a linear relationship between the two quantitative variables. For a bivariate normal distribution, numerous procedures have been proposed for testing a precise null hypothesis of the correlation coefficient, whereas the construction of flexible procedures for testing a set of (multiple) precise and/or interval hypotheses has received less attention. This paper fills the gap by proposing an objective Bayesian testing procedure using the divergence-based priors. The proposed Bayes factors can be used for testing any combination of precise and interval hypotheses and also allow a researcher to quantify evidence in the data in favor of the null or any other hypothesis under consideration. An extensive simulation study is conducted to compare the performances between the proposed Bayesian methods and some existing ones in the literature. Finally, a real-data example is provided for illustrative purposes.

中文翻译：

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基于散度的先验条件下相关系数的客观贝叶斯检验

摘要 相关系数是衡量两个定量变量之间线性关系强弱的常用标准。对于二元正态分布，已经提出了许多程序来测试相关系数的精确零假设，而构建用于测试一组（多个）精确和/或区间假设的灵活程序却很少受到关注。本文通过提出使用基于散度的先验的客观贝叶斯测试程序来填补空白。提议的贝叶斯因子可用于测试精确假设和区间假设的任何组合，并且还允许研究人员量化数据中的证据，以支持零假设或任何其他正在考虑的假设。进行了广泛的模拟研究，以比较所提出的贝叶斯方法与文献中的一些现有方法之间的性能。最后，为了说明目的，提供了一个真实数据示例。