  Stochastic reaction networks that exhibit bistability are common in many
fields such as systems biology and materials science. Sampling of the
stationary distribution is crucial for understanding and characterizing the
long term dynamics of bistable stochastic dynamical systems. However, this is
normally hindered by the insufficient sampling of the rare transitions between
the two metastable regions. In this paper, we apply the parallel replica
(ParRep) method for continuous time Markov chain to accelerate the stationary
distribution sampling of bistable stochastic reaction networks. The proposed
method uses parallel computing to accelerate the sampling of rare transitions
and it is very easy to implement. We combine ParRep with the path space
information bounds for parametric sensitivity analysis. We demonstrate the
efficiency and accuracy of the method by studying the Schl\"{o}gl model and the
genetic switches network.
