  The $H_0$ tension and the accompanying $r_d$ tension are a hot topic in
current cosmology. In order to remove the degeneracy between the Hubble
parameter $H_0$ and the sound horizon scale $r_d$ from the Baryon Acoustic
Oscillations (BAO) datasets, we redefine the likelihood by marginalizing over
the $H_0 \cdot r_d$ parameter and then we perform full Bayesian analysis for
different models of dark energy (DE). We find that our uncalibrated by early or
late physics {datasets cannot} constrain the DE models properly without further
assumptions. By adding the type IA supernova dataset, the models are
constrained better with smaller errors on the DE parameters. The two BAO
datasets we use -- one with angular measurements and one with angular and
radial ones with their covariances, show statistical preferences for different
models, with $\Lambda$CDM being the best model for one of them. Adding the
Pantheon SnIA dataset with its covariance matrix boosts the statistical
preference for $\Lambda$CDM.
