Enhancement of Natural Extension

The theory of imprecise previsions admits the use of a wide variety of statistical evidence. Nevertheless, some existing evidence, for example, in reliability applications, cannot be utilized by models developed within its framework. In the pursuit of reducing imprecision, any available evidence should become an input to modeling. It is suggested to take a different look at the natural extension, the basic constructive step in the theory. It is shown that natural extension can be viewed as a problem belonging to the realm of variational calculus, which opens up new perspectives for obtaining tighter intervals.