Computational complexity analysis for Monte Carlo approximations of classically scaled population processes
Provides a systematic complexity comparison of simulation strategies for stochastic population processes, aiding practitioners in choosing efficient methods.
The paper analyzes computational complexity of Monte Carlo methods for classically scaled population processes, including biochemical systems. It finds that multilevel Monte Carlo with diffusion approximation is most efficient when diffusion bias is smaller than required accuracy, but tau-leaping is optimal otherwise.
We analyze and compare the computational complexity of different simulation strategies for Monte Carlo in the setting of classically scaled population processes. This allows a range of widely used competing strategies to be judged systematically. Our setting includes stochastically modeled biochemical systems. We consider the task of approximating the expected value of some path functional of the state of the system at a fixed time point. We study the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an Euler-Maruyama discretization of a diffusion approximation. Appropriate modifications of recently proposed multilevel Monte Carlo algorithms are also studied for the tau-leaping and Euler-Maruyama approaches. In order to quantify computational complexity in a tractable yet meaningful manner, we consider a parameterization that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling. We base the analysis on a novel asymptotic regime where the required accuracy is a function of the model scaling parameter. Our new analysis shows that, under the specific assumptions made in the manuscript, if the bias inherent in the diffusion approximation is smaller than the required accuracy, then multilevel Monte Carlo for the diffusion approximation is most efficient, besting multilevel Monte Carlo with tau-leaping by a factor of a logarithm of the scaling parameter. However, if the bias of the diffusion model is greater than the error tolerance, or if the bias can not be bounded analytically, multilevel versions of tau-leaping are often the optimal choice.