Biased versus unbiased numerical methods for stochastic simulations

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.

References in corpus (18)

• Epidemic processes in complex networks
• The Mechanics and Statistics of Active Matter
• Multiscale mobility networks and the large scale spreading of infectious diseases
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions
• Critical Market Crashes
• Is the Voter Model a model for voters?
• Phase transitions in contagion processes mediated by recurrent mobility patterns
• Quantum stochastic processes and quantum non-Markovian phenomena
• Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
• Markovian Dynamics on Complex Reaction Networks
• The limitations of discrete-time approaches to continuous-time contagion dynamics
• Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks
• Impact of urban structure on infectious disease spreading
• Simulation of large deviation functions using population dynamics
• Gillespie algorithms for stochastic multiagent dynamics in populations and network
• On the Gaussian approximation for master equations

Cited by in corpus (2)

• Analytic and Monte Carlo Approximations to the Distribution of the First Passage Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable