  In cosmology many dramatically different scenarios with the past (big bang
versus bounce) and in the future (de Sitter versus big rip) singularities are
compatible with the present day observations. This difficulty is called the
degeneracy problem. We use the Akaike and Bayesian information criteria of
model selection to overcome this degeneracy and to determine a model with such
a set of parameters which gives the most preferred fit to the SNIa data. We
consider seven representative scenarios, namely: the CDM models with the
cosmological constant, with topological defect, with phantom field, with
bounce, with bouncing phantom field, with brane and model with the linear
dynamical equation of state parameter. Applying the model selection information
criteria we show that AIC indicates the flat phantom model while BIC indicates
both flat phantom and flat $\Lambda$CDM models. Finally we conclude that the
number of essential parameters chosen by dark energy models which are compared
with SNIa data is two.
