Sequential estimation for prescribed statistical accuracy in stochastic simulation of biological systems

Stochastic simulation of biological systems proceeds by repeatedly generating sample paths or trajectories of the underlying stochastic process, from which many relevant and important system properties can be obtained. While a great deal of research is targeted towards accelerated trajectory generation, issues concerned with the variability across trajectories are often neglected. Advanced methods for properly quantifying the statistical accuracy and determining a reasonable number of trajectories are hardly addressed formally in the context of biological system simulation, though mathematical statistics provides a large body of powerful theory. We invoke this theory and show how mathematically well-founded sequential estimation approaches serve for systematically generating enough but not too many trajectories for achieving a certain prescribed accuracy. The practical applicability is demonstrated and illustrated by numerical examples through simulation studies of an immigration-death process and a gene regulatory network.