  Network inference has been attracting increasing attention in several fields,
notably systems biology, control engineering and biomedicine. To develop a
therapy, it is essential to understand the connectivity of biochemical units
and the internal working mechanisms of the target network. A network is mainly
characterized by its topology and internal dynamics. In particular, sparse
topology and stable system dynamics are fundamental properties of many
real-world networks. In recent years, kernel-based methods have been popular in
the system identification community. By incorporating empirical Bayes, this
framework, which we call KEB, is able to promote system stability and impose
sparse network topology. Nevertheless, KEB may not be ideal for topology
detection due to local optima and numerical errors. Here, therefore, we propose
an alternative, data-driven, method that is designed to greatly improve
inference accuracy, compared with KEB. The proposed method uses dynamical
structure functions to describe networks so that the information of
unmeasurable nodes is encoded in the model. A powerful numerical sampling
method, namely reversible jump Markov chain Monte Carlo (RJMCMC), is applied to
explore full Bayesian models effectively. Monte Carlo simulations indicate that
our approach produces more accurate networks compared with KEB methods.
Furthermore, simulations of a synthetic biological network demonstrate that the
performance of the proposed method is superior to that of the state-of-the-art
method, namely iCheMA. The implication is that the proposed method can be used
in a wide range of applications, such as controller design, machinery fault
diagnosis and therapy development.
