  We used methods of Bayesian statistical inference and the principle of
maximum entropy to analytically continue imaginary-time Green's function
generated in quantum Monte Carlo simulations to obtain the real-time Green's
functions. For test problems, we considered chains of harmonic and anharmonic
oscillators whose properties we simulated by a hybrid path-integral quantum
Monte Carlo method. From the imaginary-time displacement-displacement Green's
function, we first obtained its spectral density. For harmonic oscillators, we
demonstrated the peaks of this function were in the correct position and their
area satisfied a sum rule. Additionally, as a function of wavenumber, the peak
positions followed the correct dispersion relation. For a double-well
oscillator, we demonstrated the peak location correctly predicted the tunnel
splitting. Transforming the spectral densities to real-time Green's functions,
we conclude that we can predict the real-time dynamics for length of times
corresponding to 5 to 10 times the natural period of the model. The length of
time was limited by an overbroadening of the peaks in the spectral density
caused by the simulation algorithm.
