  There are several methods for model selection in cosmology which have at
least two major goals, that of finding the correct model or predicting well. In
this work we discuss through a study of well-known model selection methods like
Akaike information criterion (AIC), Bayesian information criterion (BIC),
deviance information criterion (DIC) and Bayesian evidence, how these different
goals are pursued in each paradigm. We also apply another method for model
selection which less seen in cosmological literature, the Cross-validation
method. Using these methods we will compare two different scenarios in
cosmology, $\Lambda$CDM model and dynamical dark energy. We show that each of
the methods tends to different results in model selection. While BIC and
Bayesian evidence overrule the dynamical dark energy scenarios with 2 or 3
extra degree of freedom, the DIC and cross-validation method prefer these
dynamical models to $\Lambda$CDM model. Assuming the numerical results of
different analysis and combining cosmological and statistical aspects of the
subject, we propose cross-validation as an interesting method for model
selection in cosmology that can lead to different results in comparison with
usual methods of model selection.
