  Inferring time-varying networks is important to understand the development
and evolution of interactions over time. However, the vast majority of
currently used models assume direct measurements of node states, which are
often difficult to obtain, especially in fields like cell biology, where
perturbation experiments often only provide indirect information of network
structure. Here we propose hidden Markov nested effects models (HM-NEMs) to
model the evolving network by a Markov chain on a state space of signalling
networks, which are derived from nested effects models (NEMs) of indirect
perturbation data. To infer the hidden network evolution and unknown parameter,
a Gibbs sampler is developed, in which sampling network structure is
facilitated by a novel structural Metropolis--Hastings algorithm. We
demonstrate the potential of HM-NEMs by simulations on synthetic time-series
perturbation data. We also show the applicability of HM-NEMs in two real
biological case studies, in one capturing dynamic crosstalk during the
progression of neutrophil polarisation, and in the other inferring an evolving
network underlying early differentiation of mouse embryonic stem cells.
