We propose an objective non-local prior for testing symmetry against skew-symmetric alternatives. The prior is derived through a formal construction rule by assigning a uniform distribution to a discrepancy-based measure of the shape parameter's effect. This approach avoids the need for user-specified hyperparameters and produces a weakly informative prior tailored to the skew-symmetric family. We illustrate the use of the proposed prior in the context of testing normality against skew-normal alternatives through both a simulation study and a real-data application.

翻译：本文提出了一种用于检验对称性相对于偏斜对称备择假设的客观非局部先验。该先验通过形式化构造规则推导得出，其方法是对基于差异的形状参数效应度量赋予均匀分布。此方法避免了用户指定超参数的需要，并产生了一个针对偏斜对称族定制的弱信息先验。我们通过模拟研究和实际数据应用，说明了所提先验在检验正态性相对于偏斜正态备择假设的上下文中的使用。