A Bayesian comparison between $\Lambda$CDM and phenomenologically
  emergent dark energy models
  In this work we examine the recently proposed phenomenological emergent dark
energy (PEDE) model by \cite{Li:2019yem}, using the latest observational data
in both expansion and perturbation levels. Applying the statistical Bayesian
evidence as well as the AIC and BIC information criteria, we compare the PEDE
model with the concordance $\Lambda$CDM model in both flat and non-flat
universes. We combine the observational datasets as (i) expansion data (except
CMB), (ii) expansion data (including CMB) and (iii) expansion data jointed to
the growth rate dataset. Our statistical results show that the flat-
$\Lambda$CDM model is still the best model. In the case of expansion data
(including CMB), we observe that the flat- PEDE model is well consistent with
observations as well as the concordance $\Lambda$CDM universe. While in the
cases of (i) and (iii), the PEDE models in both of the flat and non-flat
geometries are not favored. In particular, we see that in the perturbation
level the PEDE model can not fit the observations as equally as standard
$\Lambda$CDM cosmology. As the ability of the model, we show that the PEDE
models can alleviate the tension of Hubble constant value appearing between the
local observations and Planck inferred estimation in standard cosmology.
