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The average spectrum method is a promising approach for the analyticcontinuation of imaginary time or frequency data to the real axis. Itdetermines the analytic continuation of noisy data from a functional averageover all admissible spectral functions, weighted by how well they fit the data.Its main advantage is the apparent lack of adjustable parameters and smoothnessconstraints, using instead the information on the statistical noise in thedata. Its main disadvantage is the enormous computational cost of performingthe functional integral. Here we introduce an efficient implementation, basedon the singular value decomposition of the integral kernel, eliminating thisproblem. It allows us to analyze the behavior of the average spectrum method indetail. We find that the discretization of the real-frequency grid, on whichthe spectral function is represented, biases the results. The distribution ofthe grid points plays the role of a default model while the number of gridpoints acts as a regularization parameter. We give a quantitative explanationfor this behavior, point out the crucial role of the default model and providea practical method for choosing it, making the average spectrum method areliable and efficient technique for analytic continuation.

The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid