  A number of modern sampling methods probe long time behavior in complex
biomolecules using a set of relatively short trajectory segments. Markov state
models (MSMs) can be useful in analyzing such data sets, but in particularly
complex landscapes, the available trajectory data may prove insufficient for
constructing valid Markov models. Here, we explore the potential utility of
history-dependent analyses applied to relatively poor decompositions of
configuration space for which MSMs are inadequate. Our approaches build on
previous work [Suarez et. al., JCTC 2014] showing that, with sufficient history
information, unbiased equilibrium and non-equilibrium observables can be
obtained even for arbitrary non-Markovian divisions of phase space. We explore
a range of non-Markovian approximations using varying amounts of history
information to model the finite length of trajectory segments, applying the
analyses to toy models as well as several proteins previously studied by
microsec-milisec scale atomistic simulations [Lindorff-Larsen et. al., Science
2011].
