title: Extending the Multi-level Method for the Simulation of Stochastic Biological Systems.
abstract: The multi-level method for discrete-state systems, first introduced by Anderson and Higham (SIAM Multiscale Model Simul 10(1):146-179, 2012), is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum, and, as such, the method has the potential to revolutionise the field of stochastic simulation. In this paper, we present several refinements of the multi-level method which render it easier to understand and implement, and also more efficient. Given the substantial and complex nature of the multi-level method, the first part of this work reviews existing literature, with the aim of providing a practical guide to the use of the multi-level method. The second part provides the means for a deft implementation of the technique and concludes with a discussion of a number of open problems.
authors: Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK. lesterc@maths.ox.ac.uk.
authors: Christopher
authors: C
authors: Lester
authors: Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK.
authors: Ruth E
authors: RE
authors: Baker
authors: Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK.
authors: Michael B
authors: MB
authors: Giles
authors: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK.
authors: Christian A
authors: CA
authors: Yates
mesh_terms: D000465:Algorithms; D001669:Biochemical Phenomena; D003198:Computer Simulation; D053263:Gene Regulatory Networks; D020935:MAP Kinase Signaling System; D055641:Mathematical Concepts; D008954:Models, Biological; D008956:Models, Chemical; D008957:Models, Genetic; D009010:Monte Carlo Method; D016012:Poisson Distribution; D013269:Stochastic Processes
keywords: Gene regulatory networks; Gillespie algorithm; Multi-level; Stochastic simulation; Tau-leaping