The interplay of Bayesian and frequentist analysis

Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. At the methodological level, however, the debate has become considerably muted, with the recognition that each approach has a great deal to contribute to statistical practice and each is actually essential for full development of the other approach. In this article, we embark upon a rather idiosyncratic walk through some of these issues.