Bayesian correction of $H(z)$ data uncertainties

We compile 41 $H(z)$ data from literature and use them to constrain O$\Lambda$CDM and flat $\Lambda$CDM parameters. We show that the available $H(z)$ suffers from uncertainties overestimation and propose a Bayesian method to reduce them. As a result of this method, using $H(z)$ only, we find, in the context of O$\Lambda$CDM, $H_0=69.5\pm2.5\mathrm{\,km\,s^{-1}Mpc^{-1}}$, $\Omega_m=0.242\pm0.036$ and $\Omega_\Lambda=0.68\pm0.14$. In the context of flat $\Lambda$CDM model, we have found $H_0=70.4\pm1.2\mathrm{\,km\,s^{-1}Mpc^{-1}}$ and $\Omega_m=0.256\pm0.014$. This corresponds to an uncertainty reduction of up to 30\% when compared to the uncorrected analysis in both cases.