  The maximum entropy method is shown to be a special limit of the stochastic
analytic continuation method introduced by Sandvik [Phys. Rev. B 57, 10287
(1998)]. We employ a mapping between the analytic continuation problem and a
system of interacting classical fields. The Hamiltonian of this system is
chosen such that the determination of its ground state field configuration
corresponds to an unregularized inversion of the analytic continuation input
data. The regularization is effected by performing a thermal average over the
field configurations at a small fictitious temperature using Monte Carlo
sampling. We prove that the maximum entropy method, the currently accepted
state of the art, is simply the mean field limit of this fully dynamical
procedure. We also describe a technical innovation: we suggest that a parallel
tempering algorithm leads to better traversal of the phase space and makes it
easy to identify the critical value of the regularization temperature.
