Model Evaluation of the Stochastic Boolean Control Networks

This paper investigates the model evaluation problem for the stochastic Boolean control networks (SBCNs). First, an algebraic expression of the SBCN is obtained based on the semi-tensor product method, and a straightforward approach is then proposed to compute the probability that the given observed output sequence is produced by the considered model. Second, two recursive algorithms, namely the forward and the backward algorithms, are designed for model evaluation by resorting to the forward-backward technique. In addition, scaling factors are introduced to deal with the numerical issues arising in the implementation of the developed algorithms. Finally, to illustrate the applicability and effectiveness of the proposed algorithms, a Boolean model of the lac operon is employed as an example for numerical simulation.