After ten years of applied Bayesian work in phylogenetics and in evolutionary genetics, I feel the need to step back and re-think the whole thing.

Undoubtedly, since its introduction in phylogenetics in the late 90's, Bayesian inference has become an essential part of current applied statistical work in evolutionary sciences. The success of Bayesian inference has several causes: computational (the possibilities offered by Monte Carlo), but also conceptual: personally, I would tend to emphasize the flexibility and the modularity offered by the Bayesian paradigm for designing more complex models.

On the other hand, there are still many problems, computational, theoretical and even foundational. There is of course the usual question of the choice of the prior, but there are many other open ends. Just think about how to conduct model comparison, selection and test: to me, this represents a particularly problematic aspect of current Bayesian applied work.

On a more foundational note, although the question has been discussed at length in the phylogenetic literature of the early 2000's, it is still not quite clear how we are supposed to interpret posterior probabilities in practice. It is not even clear in what respect much of what we are currently doing in evolutionary sciences really conforms to the 'official' Bayesian subjectivistic philosophy.

Finally, we tend to oppose frequentist and Bayesian inference and to regard them as two mutually incompatible paradigms. However, in practice, there appears to be quite some overlap between the two approaches. Some keywords here:

*empirical Bayes, statistical decision theory, calibration*. The empirical Bayes paradigm, in particular, offers an interesting synthesis, which I would like to explore in depth in future posts.

Thus, my dear Fellows, Bayesian cooks or distinguished Frequentists alike, please keep an eye on this blog and do not hesitate to join the discussion.

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