The opportunity to do statistics arises when we consider a statistical model
specified by a family
of unnormalized densities with respect to
.
The normalizing function of the family is
Recall that the requirement that
for all
is implied by using the terminology `unnormalized
density' for each of the
.
Normalized densities of the family are defined by
and the corresponding probability measures by
Models of this type include Markov point processes (Ripley and Kelley, 1977)
and nearest-neighbour Markov point processes (Baddeley and Møller, 1989).
Another broad family is exponential family models in which
has
the form
where t is a map from
to
and the parameter space
is a subset of
.