Two different numerically exact methods for open quantum system dynamics, the hierarchy of pure states (HOPS) method, and the
multi-Davydov-Ansatz are discussed. We focus on the suitability of the underlying representations of bath correlations. While in the HOPS
case the correct description of the bath correlation function (BCF) in the time domain is decisive, it turns out that a windowed Fourier trans-
form of the BCF is an appropriate indicator of the quality of the discretization in the multi-Davydov-Ansatz. For the spin-boson model with
sub-Ohmic spectral density considered here, a discretization of the spectral density based on an exponential distribution, used previously,
turns out to be most favorable