For over a decade now, other disciplines that heavily rely on analyzing empirical data—including medicine, psychology, economics, and marketing—have been in a sort of replication crisis. Among other things, this crisis originates in using inflexible or inadequate statistical practices to analyze small datasets collected in experiments conducted in conditions that poorly capture real-world scenarios, and are plagued by confounders that are hard to control. There is reason to believe software engineering might not be much better off.

Given the broad and growing interest for statistical data analysis throughout the software engineering community, we will mainly focus on:

• limitations of the current most common statistical techniques in software engineering;
• principles underlying Bayesian data analysis;
• brief overview of the Bayesian statistical framework;
• key guidelines to apply Bayesian data analysis in practice;
• practical examples of Bayesian (re-)analysis of software engineering empirical data.

Bayesian statistics is not a silver bullet that will fix all the issues with empirical data analysis (in software engineering); but it can be an important step in the direction of helping empirical software engineering build solid foundations and achieve robust results.