Probabilistic Stellar Mass and Radius Estimation with Bayesian Hierarchical Stacking

Accurate stellar parameters are essential for the characterisation of exoplanets, yet most host stars lack direct measurements of mass and radius. The new analysis still awaits peer review, but it already lays out the central claim clearly.

The significance lies in exoplanet science has moved beyond the era of simple discovery into a period of comparative characterization. With more than five thousand confirmed planets known, the scientifically productive questions now concern atmospheric composition, internal structure, orbital history and the statistical properties of populations rather than the existence of individual worlds. A new detection or spectral measurement is most valuable when it adds a well-constrained data point to those comparative frameworks, not when it stands alone as an anecdote. We aim to predict stellar masses and radii from commonly available observables and to quantify uncertainties and systematic effects in a way that is consistent with stellar. By not relying on a single model, we aim to obtain more robust predictive distributions and reduce sensitivity to model misspecification and outliers.

We develop a Bayesian machine-learning framework that combines three probabilistic models through Bayesian hierarchical stacking (BHS): a Bayesian additive regression tree model. The method propagates measurement uncertainties, accounts for correlations among inputs, and aggregates model variance into final predictive distributions.

Applied to about 2400 exoplanet host stars, the predictions differ from literature values by a MARD of 2.7% in both mass and radius. Residual analysis reveals mild underestimation for cool dwarfs, consistent with sparse training coverage, and positive offsets near the main-sequence turn-off that may reflect.

Internal consistency with g = GM/R^2 is greater for the BHS predictions, with a scatter in Delta log g lower by a factor of three than that of the literature values. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

The broader interest lies in making the target less anecdotal and more comparable with the rest of the known planetary population. Population-level questions, such as the frequency of atmospheres around small rocky planets or the prevalence of water-rich worlds in the habitable zone, require well-characterized individual data points before statistical patterns become meaningful. Each new planet with a measured radius, mass and, ideally, atmospheric constraint is a brick in that larger structure, and the accumulation of bricks eventually allows theorists to test formation models against real distributions rather than projections.

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Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to improve independent constraints on the mass, radius, atmospheric composition and orbital dynamics of the target. Transmission spectroscopy with JWST, radial velocity campaigns with high-resolution ground-based spectrographs and phase-curve measurements from space photometry represent the observational toolkit that can move characterization from plausible to robust. That convergence of techniques is the standard the community now expects before a planetary atmosphere result is treated as confirmed. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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