Hybrid chernoff tau-leap

Handle URI:
http://hdl.handle.net/10754/563319
Title:
Hybrid chernoff tau-leap
Authors:
Moraes, Alvaro ( 0000-0003-4144-1243 ) ; Tempone, Raul ( 0000-0003-1967-4446 ) ; Vilanova, Pedro ( 0000-0001-6620-6261 )
Abstract:
Markovian pure jump processes model a wide range of phenomena, including chemical reactions at the molecular level, dynamics of wireless communication networks, and the spread of epidemic diseases in small populations. There exist algorithms such as Gillespie's stochastic simulation algorithm (SSA) and Anderson's modified next reaction method (MNRM) that simulate a single path with the exact distribution of the process, but this can be time consuming when many reactions take place during a short time interval. Gillespie's approximated tau-leap method, on the other hand, can be used to reduce computational time, but it may lead to nonphysical values due to a positive one-step exit probability, and it also introduces a time discretization error. Here, we present a novel hybrid algorithm for simulating individual paths which adaptively switches between the SSA and the tau-leap method. The switching strategy is based on a comparison of the expected interarrival time of the SSA and an adaptive time step derived from a Chernoff-type bound for the one-step exit probability. Because this bound is nonasymptotic, we do not need to make any distributional approximation for the tau-leap increments. This hybrid method allows us (i) to control the global exit probability of any simulated path and (ii) to obtain accurate and computable estimates of the expected value of any smooth observable of the process with minimal computational work. We present numerical examples that illustrate the performance of the proposed method. © 2014 Society for Industrial and Applied Mathematics.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Stochastic Numerics Research Group
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
Multiscale Modeling & Simulation
Issue Date:
Jan-2014
DOI:
10.1137/130925657
Type:
Article
ISSN:
15403459
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMoraes, Alvaroen
dc.contributor.authorTempone, Raulen
dc.contributor.authorVilanova, Pedroen
dc.date.accessioned2015-08-03T11:45:38Zen
dc.date.available2015-08-03T11:45:38Zen
dc.date.issued2014-01en
dc.identifier.issn15403459en
dc.identifier.doi10.1137/130925657en
dc.identifier.urihttp://hdl.handle.net/10754/563319en
dc.description.abstractMarkovian pure jump processes model a wide range of phenomena, including chemical reactions at the molecular level, dynamics of wireless communication networks, and the spread of epidemic diseases in small populations. There exist algorithms such as Gillespie's stochastic simulation algorithm (SSA) and Anderson's modified next reaction method (MNRM) that simulate a single path with the exact distribution of the process, but this can be time consuming when many reactions take place during a short time interval. Gillespie's approximated tau-leap method, on the other hand, can be used to reduce computational time, but it may lead to nonphysical values due to a positive one-step exit probability, and it also introduces a time discretization error. Here, we present a novel hybrid algorithm for simulating individual paths which adaptively switches between the SSA and the tau-leap method. The switching strategy is based on a comparison of the expected interarrival time of the SSA and an adaptive time step derived from a Chernoff-type bound for the one-step exit probability. Because this bound is nonasymptotic, we do not need to make any distributional approximation for the tau-leap increments. This hybrid method allows us (i) to control the global exit probability of any simulated path and (ii) to obtain accurate and computable estimates of the expected value of any smooth observable of the process with minimal computational work. We present numerical examples that illustrate the performance of the proposed method. © 2014 Society for Industrial and Applied Mathematics.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectError controlen
dc.subjectError estimatesen
dc.subjectExit probabilityen
dc.subjectHybrid algorithmsen
dc.subjectTau-leapen
dc.subjectWeak approximationen
dc.titleHybrid chernoff tau-leapen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalMultiscale Modeling & Simulationen
kaust.authorMoraes, Alvaroen
kaust.authorTempone, Raulen
kaust.authorVilanova, Pedroen
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