Bayesian priors for transiting planets
Kipping et al
As astronomers push towards discovering ever-smaller transiting planets, it is increasingly common to deal with low signal-to-noise ratio (SNR) events, where the choice of priors plays an influential role in Bayesian inference. In the analysis of exoplanet data, the selection of priors is often treated as a nuisance, with observers typically defaulting to uninformative distributions. Such treatments miss a key strength of the Bayesian framework, especially in the low SNR regime, where even weak a priori information is valuable. When estimating the parameters of a low-SNR transit, two key pieces of information are known: (i) the planet has the correct geometric alignment to transit and (ii) the transit event exhibits sufficient signal-to-noise to have been detected. These represent two forms of observational bias. Accordingly, when fitting transits, the model parameter priors should not follow the intrinsic distributions of said terms, but rather those of both the intrinsic distributions and the observational biases. In this work, we derive the shape of these priors for trapezoidal transits and occultations, including the case of grazing events. These results naturally explain why the observed population shows a bias towards equatorial transits and why the observational bias of ratio-of-radii is super-quadratic, scaling as (RP/R⋆)5/2. We may account for these observational biases by adding on log likelihood penalty terms, for which we provide Python code to generate, ExoPriors.