  We present a general framework for performing "bold-line" diagrammatic Monte
Carlo calculations based on using an analytical partial resummation as a
starting point for stochastically summing all diagrams. As an example we solve
the one orbital Anderson model using the non-crossing approximation as a
starting point. We assess the accuracy of the method by using it to solve the
equations of single-site dynamical mean field theory. We establish the validity
of the starting approximations and show that the bold method provides a very
accurate treatment of the Mott-insulating phase.
