long-period exoplanets

My research day started late morning, when I met with Heather Knutson (Caltech), Marta Bryan (Caltech), and Henry Ngo (Caltech) to discuss population inferences involving long-period Jupiter-like planets. For each star, they get a velocity trend ("acceleration", I would call it) and a curvature ("jerk", I would call it), and they use these to constrain the properties of any long-period companion. We discussed what they are doing, and also my ideal vision of what is the best thing that can be done with these data.

One interesting technical point: When you have an acceleration and jerk that are both consistent with zero, do you treat them as "non-detections" or do you treat them identically with detections, and just compute the likelihood of the data given a long-period companion model? In the context of a full hierarchical model, there is no need (I think) to treat the detections and the non-detections differently. The key thing is to permit the model to include zero-mass planets or non-planets or models of differing complexity.