  Statistics comes in two main flavors: frequentist and Bayesian. For
historical and technical reasons, frequentist statistics has dominated data
analysis in the past; but Bayesian statistics is making a comeback at the
forefront of science. In this paper, we give a practical overview of Bayesian
statistics and illustrate its main advantages over frequentist statistics for
the kinds of analyses that are common in empirical software engineering, where
frequentist statistics still is standard. We also apply Bayesian statistics to
empirical data from previous research investigating agile vs. structured
development processes, the performance of programming languages, and random
testing of object-oriented programs. In addition to being case studies
demonstrating how Bayesian analysis can be applied in practice, they provide
insights beyond the results in the original publications (which used
frequentist statistics), thus showing the practical value brought by Bayesian
statistics.
