A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane. Efficient ways to construct such representations are also introduced. The performance of the algorithm is tested on small and large lattices with a $����^4$ theory with quadratic nearest-neighbor complex coupling. The method works for moderate complex couplings, reproducing reweighting and complex Langevin results and fulfilling various Schwinger-Dyson relations.

23 pages, 2 tables, 11 figure. Major revision