Aims. Using a generalized Bayesian inference method, we aim to explore the possible interior structures of six selected exoplanets for which planetary mass and radius measurements are available in addition to stellar host abundances: HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b. We aim to investigate the importance of stellar abundance proxies for the planetary bulk composition (namely Fe/Si and Mg/Si) on prediction of planetary interiors.

Methods. We performed a full probabilistic Bayesian inference analysis to formally account for observational and model uncertainties while obtaining confidence regions of structural and compositional parameters of core, mantle, ice layer, ocean, and atmosphere. We determined how sensitive our parameter predictions depend on (1) different estimates of bulk abundance constraints and (2) different correlations of bulk abundances between planet and host star.

Results. The possible interior structures and correlations between structural parameters differ depending on data and data uncertainty. The strongest correlation is generally found between size of rocky interior and water mass fraction. Given the data, possible water mass fractions are high, even for most potentially rocky planets (HD 219134b, Kepler-93b, CoRoT-7b, and 55 Cnc e with estimates up to 35%, depending on the planet). Also, the interior of Kepler-10b is best constrained with possible interiors similar to Earth. Among all tested planets, only the data of Kepler-10b and Kepler-93b allow to put a higher probability on the planetary bulk Fe/Si to be stellar compared to extremely sub-stellar.

Conclusions. Although the possible ranges of interior structures are large, structural parameters and their correlations are constrained by the sparse data. The probability for the tested exoplanets to be Earth-like is generally very low. Furthermore, we conclude that different estimates of planet bulk abundance constraints mainly affect mantle composition and core size.