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

Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation