Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepan...

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Bibliographic Details
Published in:Bulletin of mathematical biology Vol. 81; no. 8; pp. 2931 - 2959
Main Authors: Beentjes, Casper H. L., Baker, Ruth E.
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2019
Springer Nature B.V
Subjects:
Algorithms
Biochemical Phenomena
Biological effects
Cell Biology
Chemical reactions
Computer Simulation
Convergence
Decay rate
Differential equations
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematical models
Mathematics
Mathematics and Statistics
Models, Biological
Models, Chemical
Monte Carlo Method
Monte Carlo simulation
Organic chemistry
Random numbers
Special Issue: Gillespie and his Algorithms
Stochastic Processes
System effectiveness
Systems Biology
Stochastic simulation
Monte Carlo methods
Quasi-Monte Carlo
Tau-leaping
Variance reduction
Chemical reaction networks
ISSN:0092-8240, 1522-9602, 1522-9602
Online Access:Get full text
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Summary:Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow O ( N - 1 / 2 ) convergence rates as a function of the number of sample paths N . This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely τ -leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature.
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-018-0442-2