An adaptive multilevel simulation algorithm for stochastic biological systems
Discretestate, continuoustime Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tauleap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multilevel method [Anderson and Higham, “Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders themore »
 Authors:

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 Mathematical Institute, Woodstock Road, Oxford OX2 6GG (United Kingdom)
 Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22415823
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ALGORITHMS; ANALYTICAL SOLUTION; APPROXIMATIONS; COMPARATIVE EVALUATIONS; CORRECTIONS; MARKOV PROCESS; MONTE CARLO METHOD; RANDOMNESS; STATISTICS