The situation does not get much worse when the the distribution of the
complete data (x, y) is specified by a family of unnormalized densities
. Let
be the unknown normalizing function for the joint density.
Following our slogan, 
is not only an unnormalized joint density
for x and y but also an unnormalized conditional density of x given
y (or y given x). The normalizing functions are different, but the
same function serves in both capacities. Considered an unnormalized
conditional density the normalizing constant is
Now the likelihood is
a ratio of two normalizing functions. As we shall see this still permits Monte Carlo likelihood inference.