  We describe a simple form of importance sampling designed to bound and
compute large-deviation rate functions for time-extensive dynamical observables
in continuous-time Markov chains. We start with a model, defined by a set of
rates, and a time-extensive dynamical observable. We construct a reference
model, a variational ansatz for the behavior of the original model conditioned
on atypical values of the observable. Direct simulation of the reference model
provides an upper bound on the large-deviation rate function associated with
the original model, an estimate of the tightness of the bound, and, if the
ansatz is chosen well, the exact rate function. The exact rare behavior of the
original model does not need to be known in advance. We use this method to
calculate rate functions for currents and counting observables in a set of
network- and lattice models taken from the literature. Straightforward ansatze
yield bounds that are tighter than bounds obtained from Level 2.5 of large
deviations via approximations that involve uniform scalings of rates. We show
how to correct these bounds in order to recover the rate functions exactly. Our
approach is complementary to more specialized methods, and offers a physically
transparent framework for approximating and calculating the likelihood of
dynamical large deviations.
