results and discussion

IMHO, a paper should not have a conclusions section. That's what the abstract is for! That said, many of my most trusted and respected colleagues disagree (including, for example, Johnston). My view is that the final section should be a "discussion" in which the results are put in the context of other work, evaluated and criticized. That last point is the most important: You only understand what your results are when you understand how they could be wrong. Indeed, a critical examination of the results in light of the assumptions makes both the assumptions and the results more clear.

Foreman-Mackey and I spent a lot of time on these issues today as he finishes his exoplanet population paper. Foreman-Mackey's assumptions are very strong, of course, although we argue that they are weaker than those of any other study in this area. One of the things I love about principled probabilistic inference is that it makes it very easy (or almost necessary) to be explicit about your assumptions. In related news, Foreman-Mackey argues that three independent groups now—despite making very different assumptions—have obtained very similar results on the exoplanet radius distribution at Earth-ish radii, so those results are very likely correct (or, conceivably indicative of a problem with Kepler, which is a common component of all three).