To study the dynamic properties of complex biological systems, mathematical modeling has been used widely in systems biology. Apart from the well-established knowledge for modeling techniques, there are still some difficulties while understanding the dynamics in system biology. One of the major challenges is how to infer unknown parameters in mathematical models based on the experimentally observed data sets. This is extremely difficult when the experimental data are sparse and the biological systems are stochastic. To tackle this problem, in this work we revised one computation method for inference called approximate Bayesian computation (ABC) and conducted extensive computing tests to examine the influence of a number of factors on the performance of ABC. Based on simulation results, we found that the number of stochastic simulations and step size of the observation data have substantial influence on the estimation accuracy. We applied the ABC method to two stochastic systems to test the efficiency and effectiveness of the ABC and obtained promising approximation for the unknown parameters in the systems. This work raised a number of important issues for designing effective inference methods for estimating rate constants in biochemical reaction systems.
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