  Recent astronomical observations indicate that the Universe is presently
almost flat and undergoing a period of accelerated expansion. Basing on
Einstein's general relativity all these observations can be explained by the
hypothesis of a dark energy component in addition to cold dark matter (CDM).
Because the nature of this dark energy is unknown, it was proposed some
alternative scenario to explain the current accelerating Universe. The key
point of this scenario is to modify the standard FRW equation instead of
mysterious dark energy component. The standard approach to constrain model
parameters, based on the likelihood method, gives a best-fit model and
confidence ranges for those parameters. We always arbitrary choose the set of
parameters which define a model which we compare with observational data.
Because in the generic case, the introducing of new parameters improves a fit
to the data set, there appears the problem of elimination of model parameters
which can play an insufficient role. The Bayesian information criteria of model
selection (the AIC and BIC) are dedicated to promotion a set of parameters
which should be incorporated to the model. We divide class of all accelerating
cosmological models into two groups according to the two types of explanation
acceleration of the Universe. Then the Bayesian framework of model selection is
used to determine the set of parameters which gives preferred fit to the SNIa
data. We find a few of flat cosmological models which can be recommend by both
the Bayes factor and Akaike information criterion.
