long-period planets, regularizing with informative priors

Today was a day of phone calls. The first was with Dan Foreman-Mackey, in which we discussed his results on single transits in the Kepler data (that is, planet transits where the orbital period is comparable to or longer than the Kepler mission lifetime). His approach is what you might call a probabilistic expert system: He detects anomalies in the light-curve and then competes various generative models for each anomaly. These models include exoplanet transits, but also many kinds of data defects and stellar events. In every case, he is using a flexible Gaussian-process noise model and permitting the hyper-parameters of that to vary, so it is computationally non-trivial. He has found many new single transits, including some in systems with known shorter-period planets.

This was followed by a call with Andy Casey, Melissa Ness, and Hans-Walter Rix, on the subject of regularizing The Cannon with prior information. Casey and I are looking at L1, which says that sparser models are more likely. Ness is looking at hand-tuning which wavelengths can be affected by which labels, using priors from physical models of stars (or, really, atomic physics). In both cases, we see that the priors have big effects, but we don't yet know what works best, and we expect it to be different for different stars and different chemical abundances.