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1 Refining the Weighted Stochastic Simulation Algorithm Dan T Gillespie a Dan T Gillespie Consulting 30504 Cordoba Pl Castaic California 91384 Min Roh and Linda R Petzold Department of Computer Science University of California Santa Barbara Santa Barbara California 93106 Abstract The weighted stochastic simulation algorithm wSSA recently introduced by Kuwahara and Mura J Chem Phys 129 165101 2008 is an innovative variation on the stochastic simulation algorithm SSA It enables one to estimate with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications The paper also attempts to clarify some theoretical issues connected with the wSSA including its connection to first passage time theory and its relation to the SSA Version of 20 Mar 2009 To appear in Journal of Chemical Physics 2 I I TRODUCTIO The weighted stochastic simulation algorithm wSSA recently introduced by 1 Kuwahara and Mura is an innovative variation on the standard stochastic simulation algorithm SSA which enables one to efficiently estimate the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small and the event is therefore rare The difficulty of doing this with the standard SSA has long been recognized as a limitation of the Monte Carlo simulation approach so the wSSA is a welcomed development The implementation of the wSSA described in Ref 1 does not however offer a convenient way to assess the accuracy of its probability estimate In this paper we show how a simple refinement of the original wSSA procedure allows estimating a confidence interval for its estimate of the probability This in turn as we will also show



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