Abstract Circular data are data measured in angles or directions, which occur in a wide variety of scientific fields. An often investigated hypothesis is that of circular uniformity, or isotropy. Frequentist methods for assessing the circular uniformity null hypothesis exist, but do not allow the user faced with an insignificant result to distinguish lack of power from support for the null hypothesis. Bayesian hypothesis tests, which solve this issue and several others, are developed here. They are easy to compute and perform well, which is shown in a simulation. Two alternative hypotheses are considered. One is based on the von Mises distribution and performs well against unimodal alternatives. Another is based on a kernel density, which acts as an omnibus test against all other scenarios. Assessing the performance of the tests using different priors, it is shown that they are powerful and allow more elaborate conclusions than classical tests of circular uniformity.

中文翻译：

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圆形均匀性的贝叶斯检验

摘要 圆形数据是在角度或方向上测量的数据，广泛应用于各种科学领域。一个经常研究的假设是圆形均匀性或各向同性的假设。存在用于评估圆形均匀性零假设的频率论方法，但不允许用户面临微不足道的结果来区分缺乏功效与对零假设的支持。贝叶斯假设检验解决了这个问题和其他几个问题，在这里开发。它们易于计算且性能良好，如仿真所示。考虑了两种替代假设。一种基于 von Mises 分布，并且在对抗单峰替代方案时表现良好。另一种是基于内核密度，它作为针对所有其他场景的综合测试。