Statistical Models for the Analysis of Optimization Algorithms with Benchmark Functions

Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these frequentist tools have often been misused, without testing for the statistical test assumptions, without control for family-wise 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 paper provides three main contributions. First, we motivate the need for utilizing Bayesian data analysis and provide an overview to this topic. Second, we discuss the practical aspects of BDA to ensure that our models are valid and the results 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 paper, including the code for the statistical models, the data transformations and the discussed tables and figures.