The log-likelihood 
of the empirical distribution 
as predicted by
a model p is defined by
It is easy to check that the dual function 
of the previous
section is, in fact, just the log-likelihood for the exponential model
; that is
where 
has the parametric form of (11). With
this interpretation, the result of the previous section can be rephrased as:
The modelwith maximum entropy is the model in the parametric family
that maximizes the likelihood of the training sample
.
This result provides an added justification for the maximum entropy principle:
if the notion of selecting a model 
on the basis of maximum entropy
isn't compelling enough, it so happens that this same 
is also the
model which, from among all models of the same parametric form
(11), can best account for the training sample.
