  We give an overview of statistical models and likelihood, together with two
of its variants: penalized and hierarchical likelihood. The Kullback-Leibler
divergence is referred to repeatedly, for defining the misspecification risk of
a model, for grounding the likelihood and the likelihood crossvalidation which
can be used for choosing weights in penalized likelihood. Families of penalized
likelihood and sieves estimators are shown to be equivalent. The similarity of
these likelihood with a posteriori distributions in a Bayesian approach is
considered.
