Bayesian Model Comparison of $R_h=ct$ versus $\mathrm{\Lambda }$CDM using HII galaxy Hubble diagram

We complement a recent analysis comparing $R_{\mathrm{h}}=ct$ with $\mathrm{\Lambda }$CDM/$w$CDM using HII galaxies and giant extragalactic HII regions, by carrying out Bayesian model comparison. For this purpose, we calculate the Bayes factors for $R_{\mathrm{h}}=ct$ compared to flat $\mathrm{\Lambda }$CDM/$w$CDM using the same dataset. When we use uniform priors on cosmological parameters, we find that the Bayes factors are close to 1, implying that $R_{\mathrm{h}}=ct$ is equally favored compared to $\mathrm{\Lambda }$CDM/$w$CDM. However, when we use normal priors on cosmological parameters based on Planck cosmology, we find that $R_{\mathrm{h}}=ct$ is strongly favored over flat $\mathrm{\Lambda }$CDM, while $R_{\mathrm{h}}=ct$ is marginally favored over flat $w$CDM.