SIMBAD references

The relationship between mass and radius (M-R relation) is the key for inferring the planetary compositions and thus valuable for the studies of formation and migration models. However, the M-R relation alone is not enough for planetary characterization due to the dependence of it on other confounding variables. This paper provides a non-trivial extension of the M-R relation by including the incident flux as an additional variable. By using Bayesian hierarchical modelling (BHM) that leverages the flexibility of finite mixture models, a probabilistic mass-radius-flux relationship (M-R-F relation) is obtained based on a sample of 319 exoplanets. We find that the flux has non-negligible impact on the M-R relation, while such impact is strongest for hot Jupiters. On the population level, the planets with higher level of flux tend to be denser, and high flux could trigger significant mass loss for plants with radii larger than 13R_⊕. As a result, failing to account for the flux in mass prediction would cause systematic over- or underestimation. With the recent advent of computing power, although a lot of complex statistical models can be fitted using Monte Carlo methods, it has largely remained illusive how to validate these complex models when the data are observed with large measurement errors. We present two novel methods to examine model assumptions, which can be used not only for the models we present in this paper but can also be adapted for other statistical models.