Frequentist statistical methods, such as hypothesis testing, are standard practices in studies that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test assumptions or without controlling for familywise errors in multiple group comparisons, among several other problems. Bayesian data analysis (BDA) addresses many of the previously mentioned shortcomings but its use is not widely spread in the analysis of empirical data in the evolutionary computing community. This article provides three main contributions. First, we motivate the need for utilizing BDA and provide an overview of this topic. Second, we discuss the practical aspects of BDA to ensure that our models are valid and the results are transparent. Finally, we provide five statistical models that can be used to answer multiple research questions. The online Appendix provides a step-by-step guide on how to perform the analysis of the models discussed in this article, including the code for the statistical models, the data transformations, and the discussed tables and figures.

中文翻译：

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使用基准函数分析优化算法的统计模型

频率论统计方法，例如假设检验，是提供基准比较的研究中的标准做法。不幸的是，这些方法经常被误用，例如，没有测试它们的统计测试假设或没有控制多组比较中的家庭错误，以及其他几个问题。贝叶斯数据分析 (BDA) 解决了前面提到的许多缺点，但它的使用在进化计算社区的经验数据分析中并未广泛传播。本文提供了三个主要贡献。首先，我们激发了使用 BDA 的必要性，并提供了该主题的概述。其次，我们讨论了 BDA 的实际方面，以确保我们的模型有效并且结果是透明的。最后，我们提供了五种统计模型，可用于回答多个研究问题。在线附录提供了有关如何对本文中讨论的模型进行分析的分步指南，包括统计模型的代码、数据转换以及讨论的表格和图形。