  Recent astronomical observations of SNIa, CMB, as well as BAO in the Sloan
Digital Sky Survey, suggest that the current Universe has entered a stage of an
accelerated expansion with the transition redshift at $z \simeq 0.5$. While the
simplest candidates to explain this fact is cosmological constant/vacuum
energy, there exists a serious problem of coincidence. In theoretical cosmology
we can find many possible approaches alleviating this problem by applying new
physics or other conception of dark energy. We consider state of art candidates
for the description of accelerating Universe in the framework of the Bayesian
model selection. We point out advantages as well as troubles of this approach.
We find that the combination of four data bases gives a stringent posterior
probability of the $\Lambda$CDM model which is 74%. This fact is a quantitative
exemplification of a turmoil in modern cosmology over the $\Lambda$ problem.
