  Statistics comes in two main flavors: frequentist and Bayesian. For
historical and technical reasons, frequentist statistics have traditionally
dominated empirical data analysis, and certainly remain prevalent in empirical
software engineering. This situation is unfortunate because frequentist
statistics suffer from a number of shortcomings---such as lack of flexibility
and results that are unintuitive and hard to interpret---that curtail their
effectiveness when dealing with the heterogeneous data that is increasingly
available for empirical analysis of software engineering practice.
  In this paper, we pinpoint these shortcomings, and present Bayesian data
analysis techniques that provide tangible benefits---as they can provide
clearer results that are simultaneously robust and nuanced. After a short,
high-level introduction to the basic tools of Bayesian statistics, we present
the reanalysis of two empirical studies on the effectiveness of automatically
generated tests and the performance of programming languages. By contrasting
the original frequentist analyses with our new Bayesian analyses, we
demonstrate the concrete advantages of the latter. To conclude we advocate a
more prominent role for Bayesian statistical techniques in empirical software
engineering research and practice.
