  We consider the problem of estimating the dynamic latent states of an
intracellular multiscale stochastic reaction network from time-course
measurements of fluorescent reporters. We first prove that accurate solutions
to the filtering problem can be constructed by solving the filtering problem
for a reduced model that represents the dynamics as a hybrid process. The model
reduction is based on exploiting the time-scale separations in the original
network, and it can greatly reduce the computational effort required to
simulate the dynamics. This enables us to develop efficient particle filters to
solve the filtering problem for the original model by applying particle filters
to the reduced model. We illustrate the accuracy and the computational
efficiency of our approach using a numerical example.
