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tokens: prior odds ( Jeffreys 1998 ): Here, and denote the hypothesis of validity of the direct and non-direct abundance proxy, respectively, and the probability represents how well some data are explained under the assumption of a hypothesis . Instead of the Bayes factor integral we use the maximum likelihood estimate. We obtain -values around , except for Kepler-93b and Kepler-10b with -values of . This means that only for Kepler-93b and Kepler-10b, there is a strong evidence that the direct abundance proxy better explains the planetary mass and radius. Generally, it will be very difficult to study the validity of a direct correlation of relative bulk abundances between star and hosted exoplanet given usual data uncertainties. Further studies on solar system objects are needed to improve our understanding of such abundance correlations and their dependence on planet formation history. 5. Discussion of the assumptions The success of an inference method is subject to the limitations and assumptions of the forward function . Firstly, we consider pure iron cores, which may lead to a systematic overestimation of core density and thus an underestimation of core size, if volatile compounds in the core are significant. The trade-off between predicted and independently inferred core sizes can be on the order of few to tens of percents, as shown for the terrestrial solar system planets in Dorn et al. (2015) . Secondly, our approach assumes sub-solidus conditions for core and mantle as well as a perfectly known EoS parameters for all considered compositions. For the six exoplanets considered here, their pressures and temperatures exceed the ranges for which these parameters can be measured in the laboratory. Clearly, extrapolations introduce uncertainty. Thirdly, we have assumed pure water composition of the ice layer, but other compounds such as CO, CO, CH, NH, etc. are also possible since the additional elements are relatively abundant. We have used water as a proxy for these volatiles in general because (1) oxygen is more abundant than carbon and nitrogen in the universe, and (2) water condenses at higher temperatures than ammonia and methane. Fourthly, our atmospheric model uses prescribed opacities of Jin et al. (2014) , which is suitable for solar abundances. In this aspect, the prescription is therefore not self-consistent with the non-solar metallicity cases we present in this work. We have checked that using different infrared and/or visible opacities can introduce errors in radius of 5%. Models that compute line-by-line opacities with their corresponding atmospheric abundances should be performed in the future to compute planetary radii in a self-consistent way. Another aspect is our assumption of ideal gas behavior. We have checked that for atmospheric mass fractions (/) of up to 1%, the difference in the radius between using the Saumon et al. (1995) EOS and ideal gas (for H-He atmospheres) can reach 10%. For the vast majority of our results,