Bayesian analysis

I have been a light user of Stan and RStan for some time and while there are a lot of things I really like about the language (such as the awesome community you can turn to for support and ShinyStan for inspecting Stan output) there are also a few things that I find frustrating.

Update Jan, 2022: Since this post was published in May 2020, Gelman and Carpenter (2020) have published a more comprehensive analysis on how to adjust for test imperfections using a Bayesian approach which goes beyond many of the ideas here.

The typical approach to power calculations goes something like this: first, the evaluator estimates the smallest MDE for which the intervention would be cost-effective. Second, the evaluator calculates the sample required to detect that MDE.