  We present a hybrid model of a biological filter, a genetic circuit which
removes fast fluctuations in the cell's internal representation of the extra
cellular environment. The model takes the classic feed-forward loop (FFL) motif
and represents it as a network of continuous protein concentrations and binary,
unobserved gene promoter states. We address the problem of statistical
inference and parameter learning for this class of models from partial,
discrete time observations. We show that the hybrid representation leads to an
efficient algorithm for approximate statistical inference in this circuit, and
show its effectiveness on a simulated data set.
