Parameter estimation in nonlinear chemical and biological processes with unmeasured variables from small data sets

We propose an algorithm for parameter estimation in nonlinear chemical and biological stochastic processes with unmeasured variables and small data sets. The algorithm relies on an iterative approach wherein random samples of parameters and unmeasured variables are generated, from their respective posterior density functions, through Markov chain Monte Carlo simulations. The random samples are then used in approximating the posterior density functions of the parameters. The effectiveness of the algorithm is demonstrated through two biological examples—a feed-forward loop genetic regulatory network and a JAK–STAT signal transduction pathway.