  It is an old idea to replace averages of observables with respect to a
complex weight by expectation values with respect to a genuine probability
measure on complexified space. This is precisely what one would like to get
from complex Langevin simulations. Unfortunately, these fail in many cases of
physical interest. We will describe method of deriving positive representations
by matching of moments and show simple examples of successful constructions. It
will be seen that the problem is greatly underdetermined.
