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Incorporating postleap checks in tau-leaping David F. Andersona

Summary: Incorporating postleap checks in tau-leaping
David F. Andersona
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
Received 6 July 2007; accepted 7 November 2007; published online 5 February 2008
By explicitly representing the reaction times of discrete chemical systems as the firing times of
independent, unit rate Poisson processes, we develop a new adaptive tau-leaping procedure. The
procedure developed is novel in that accuracy is guaranteed by performing postleap checks. Because
the representation we use separates the randomness of the model from the state of the system, we
are able to perform the postleap checks in such a way that the statistics of the sample paths
generated will not be biased by the rejections of leaps. Further, since any leap condition is ensured
with a probability of one, the simulation method naturally avoids negative population values.
2008 American Institute of Physics. DOI: 10.1063/1.2819665
The procedure developed in this paper is a tau-leaping
method for simulating the evolution of discrete stochastic
chemical systems. The novelty of the procedure is that a
postleap check is performed after each step in order to guar-
antee accuracy. Postleap checks have been avoided in the
past because of the worry that rejecting leaps will bias the
statistics of the sample paths. This problem is bypassed in


Source: Anderson, David F. - Department of Mathematics, University of Wisconsin at Madison


Collections: Mathematics