  The mean first-passage time (MFPT) is one standard measure for the reaction
time in thermally activated barrier-crossing processes. While the relationship
between MFPTs and phenomenological rate coefficients is known for systems that
satisfy Markovian dynamics, it is not clear how to interpret MFPTs for
experimental and simulation time-series data generated by non-Markovian
systems. Here, we simulate a one-dimensional generalized Langevin equation
(GLE) in a bistable potential and compare two related numerical methods for
evaluating MFPTs: one that only incorporates information about first arrivals
between subsequent states and is equivalent to calculating the waiting time, or
dwell time, and one that incorporates information about all first-passages
associated with a given barrier-crossing event and is therefore typically
employed to enhance numerical sampling. In the Markovian limit, the two methods
are equivalent. However, for significant memory times, the two methods suggest
dramatically different reaction kinetics. By focusing on first-passage
distributions, we systematically reveal the influence of memory-induced rapid
state-recrossing on the MFPTs, which we compare to various other numerical or
theoretical descriptions of reaction times. Overall, we demonstrate that it is
necessary to consider full first-passage distributions, rather than just the
mean barrier-crossing kinetics when analyzing non-Markovian time series data.
