  Complex weights appear in Physics which are beyond a straightforward
importance sampling treatment, as required in Monte Carlo calculations. This is
the well-known sign problem. The complex Langevin approach amounts to
effectively construct a posi\-tive distribution on the complexified manifold
reproducing the expectation values of the observables through their analytical
extension. Here we discuss the direct construction of such positive
distributions paying attention to their localization on the complexified
manifold. Explicit localized repre\-sentations are obtained for complex
probabilities defined on Abelian and non Abelian groups. The viability and
performance of a complex version of the heat bath method, based on such
representations, is analyzed.
