Biased versus unbiased numerical methods for stochastic simulations.

Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages. The binomial method, and similar approximations, are often used for numerical simulations of population models in mathematical epidemiology and ecology. The authors study the binomial method to approximate a stochastic dynamic and compare it with an unbiased Gillespie method for stochastic simulation deriving insights on optimal discretization schemes for the binomial method and provide corresponding rules that would indicate if binomial or unbiased solution methods are more efficient. [ABSTRACT FROM AUTHOR]