In a blast from the past, James Long (TAMU) called me today to discuss a re-start of what I like to call the "insane robot" project, in which we are fitting photometric data censored by an unknown (but assumed stationary) probabilistic process. This project was started with Joey Richards (wise.io), who wrote much of the code with Long's help, but it has been dormant for some time now. One astonishing thing, after a couple years of disuse, the code was comprehensible and ran successfully. Let's hear it for well-documented, well-structured code!
Late in the day, Foreman-Mackey proposed a very simple approach to inferring exoplanet population parameters, based only on the content of the Kepler "Object of Interest" catalog. That is, a way to build a probabilistic model of this catalog that would be responsible and rigorous (though involving many simplifying assumptions, of course). It relates to projects by Subo Dong and others, who have been doing approximations to hierarchical inference; one goal would be to test those conclusions. The common theme between the exoplanet project and the insane robot project is that both require a parameterized model of the completeness or data censoring; we don't know with any reliability in either case the conditions under which an observation makes it into the catalog.