Biased versus unbiased numerical methods for stochastic simulations

TL;DR

This paper compares biased and unbiased numerical methods for stochastic simulations, deriving error scaling relations and guidelines to optimize computational efficiency based on precision requirements.

Contribution

It introduces scaling relations for approximation errors and provides rules to select the most efficient method depending on desired accuracy.

Findings

Derived error scaling relations for binomial approximation methods

Provided rules to optimize discretization time and number of realizations

Established criteria to choose between biased and unbiased methods based on precision

Abstract

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.