Improving exoplanet mass characterisation with Bayesian model selection using the Learned Harmonic Mean Estimator

Abstract

Radial velocity (RV) analyses require modelling choices (such as eccentricity treatment, noise model, velocity trends, and number of planets) that can significantly affect derived planetary masses. Current practice often relies on information criteria to compare and select models, but these have known limitations: they lack the built-in Occam's razor of Bayesian model comparison, and they do not incorporate prior information. Computing the Bayesian evidence needed for Bayes factor model comparison has traditionally required dedicated algorithms such as nested sampling. The learned harmonic mean estimator (LHME) offers an alternative, estimating the Bayesian evidence directly from MCMC posterior samples, with less computational cost and with no modification to the fitting procedure. We present the first application of the LHME to RV model selection, fitting 18 model variants -- comparing circular and eccentric orbits, white noise and Gaussian Process noise models, and long-term velocity trends -- to six single-planet systems, and 72 variants to a seventh system for an $N$ versus $N+1$ planet model comparison. We find that no single model is universally preferred, reinforcing the need for model comparison to select the most appropriate model for a system, thereby ensuring robust mass characterisation. The LHME, implemented in the open-source harmonic package, makes rigorous Bayesian model comparison accessible to existing MCMC-based RV workflows, and we encourage its wider use for other model comparisons in astrophysics.