  We present the Bayesian analysis of four different types of backreation
models, which are based on the Buchert equations. In this approach, one
considers a solution to the Einstein equations for a general matter
distribution and then an average of various observable quantities is taken.
Such an approach became of considerable interest when it was shown that it
could lead to agreement with observations without resorting to dark energy. In
this paper we compare the LambdaCDM model and the backreation models with SNIa,
BAO, and CMB data, and find that the former is favoured. However, the tested
models were based on some particular assumptions about the relation between the
average spatial curvature and the backreaction, as well as the relation between
the curvature and curvature index. In this paper we modified the latter
assumption, leaving the former unchanged. We find that, by varying the relation
between the curvature and curvature index, we can obtain a better fit.
Therefore, some further work is still needed -- in particular the relation
between the backreaction and the curvature should be revisited in order to
fully determine the feasibility of the backreaction models to mimic dark
energy.
