Variance decomposition in stochastic simulators

Le Maître, O. P.; Knio, O. M.; Moraes, A.

doi:10.1063/1.4922922

Title: Variance decomposition in stochastic simulators

Authors:

Le Maître, O. P. ^[1]; Knio, O. M. ^[2]; Moraes, A. ^[3]

LIMSI-CNRS, UPR 3251, Orsay, France
Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

Publication Date:: Tue Jun 30 00:00:00 EDT 2015

Sponsoring Org.:: USDOE

OSTI Identifier:: 1228651

Grant/Contract Number:: SC0008789

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: The Journal of Chemical Physics

Additional Journal Information:: Journal Name: The Journal of Chemical Physics Journal Volume: 142 Journal Issue: 24; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics

Country of Publication:: United States

Language:: English

Citation Formats


                    Le Maître, O. P., Knio, O. M., and Moraes, A. Variance decomposition in stochastic simulators.  United States: N. p., 2015. 
Web.  doi:10.1063/1.4922922.

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                    Le Maître, O. P., Knio, O. M., & Moraes, A. Variance decomposition in stochastic simulators.  United States.  https://doi.org/10.1063/1.4922922

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                    Le Maître, O. P., Knio, O. M., and Moraes, A. Tue .  
"Variance decomposition in stochastic simulators".  United States.  https://doi.org/10.1063/1.4922922.

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@article{osti_1228651,

  title        = {Variance decomposition in stochastic simulators},

  author       = {Le Maître, O. P. and Knio, O. M. and Moraes, A.},

  abstractNote = {},

  doi          = {10.1063/1.4922922},

  journal      = {The Journal of Chemical Physics},

  number       = 24,

  volume       = 142,

  place        = {United States},

  year         = {Tue Jun 30 00:00:00 EDT 2015},

  month        = {Tue Jun 30 00:00:00 EDT 2015}

}

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Works referenced in this record:

Polynomial chaos expansion for sensitivity analysis
journal, July 2009

Crestaux, Thierry; Le Maıˆtre, Olivier; Martinez, Jean-Marc
Reliability Engineering & System Safety, Vol. 94, Issue 7
DOI: 10.1016/j.ress.2008.10.008

Bayesian Inference of Spectral Expansions for Predictability Assessment in Stochastic Reaction Networks
journal, October 2009

Sargsyan, Khachik; Debusschere, Bert; Najm, Habib
Journal of Computational and Theoretical Nanoscience, Vol. 6, Issue 10
DOI: 10.1166/jctn.2009.1285

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation
journal, January 2012

Rizzi, F.; Najm, H. N.; Debusschere, B. J.
Multiscale Modeling & Simulation, Vol. 10, Issue 4
DOI: 10.1137/110853169

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
journal, July 2013

Alexanderian, Alen; Rizzi, Francesco; Rathinam, Muruhan
Journal of Scientific Computing, Vol. 58, Issue 3
DOI: 10.1007/s10915-013-9745-5

Importance measures in global sensitivity analysis of nonlinear models
journal, April 1996

Homma, Toshimitsu; Saltelli, Andrea
Reliability Engineering & System Safety, Vol. 52, Issue 1
DOI: 10.1016/0951-8320(96)00002-6

A Class of Statistics with Asymptotically Normal Distribution
journal, September 1948

Hoeffding, Wassily
The Annals of Mathematical Statistics, Vol. 19, Issue 3
DOI: 10.1214/aoms/1177730196

Hybrid Chernoff Tau-Leap
journal, January 2014

Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro
Multiscale Modeling & Simulation, Vol. 12, Issue 2
DOI: 10.1137/130925657

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks
journal, January 2010

Rathinam, Muruhan; Sheppard, Patrick W.; Khammash, Mustafa
The Journal of Chemical Physics, Vol. 132, Issue 3
DOI: 10.1063/1.3280166

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore
journal, May 2013

Rizzi, F.; Jones, R. E.; Debusschere, B. J.
The Journal of Chemical Physics, Vol. 138, Issue 19
DOI: 10.1063/1.4804666

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels
journal, March 2000

Gibson, Michael A.; Bruck, Jehoshua
The Journal of Physical Chemistry A, Vol. 104, Issue 9
DOI: 10.1021/jp993732q

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters
journal, May 2013

Rizzi, F.; Jones, R. E.; Debusschere, B. J.
The Journal of Chemical Physics, Vol. 138, Issue 19
DOI: 10.1063/1.4804669

A rigorous derivation of the chemical master equation
journal, September 1992

Gillespie, Daniel T.
Physica A: Statistical Mechanics and its Applications, Vol. 188, Issue 1-3
DOI: 10.1016/0378-4371(92)90283-V

Approximate accelerated stochastic simulation of chemically reacting systems
journal, July 2001

Gillespie, Daniel T.
The Journal of Chemical Physics, Vol. 115, Issue 4
DOI: 10.1063/1.1378322

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics
journal, January 2012

Anderson, David F.; Higham, Desmond J.
Multiscale Modeling & Simulation, Vol. 10, Issue 1
DOI: 10.1137/110840546

Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis
journal, November 2012

Sargsyan, Khachik; Safta, Cosmin; Debusschere, Bert
IEEE/ACM Transactions on Computational Biology and Bioinformatics, Vol. 9, Issue 6
DOI: 10.1109/TCBB.2012.107

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems
journal, January 2012

Sheppard, Patrick W.; Rathinam, Muruhan; Khammash, Mustafa
The Journal of Chemical Physics, Vol. 136, Issue 3
DOI: 10.1063/1.3677230

Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters
journal, January 2012

Rizzi, F.; Najm, H. N.; Debusschere, B. J.
Multiscale Modeling & Simulation, Vol. 10, Issue 4
DOI: 10.1137/110853170

Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs
journal, May 2010

Li, Genyuan; Rabitz, Herschel; Yelvington, Paul E.
The Journal of Physical Chemistry A, Vol. 114, Issue 19
DOI: 10.1021/jp9096919

PC analysis of stochastic differential equations driven by Wiener noise
journal, March 2015

Le Maître, O. P.; Knio, O. M.
Reliability Engineering & System Safety, Vol. 135
DOI: 10.1016/j.ress.2014.11.002

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems
journal, January 2015

Wolf, Elizabeth Skubak; Anderson, David F.
The Journal of Chemical Physics, Vol. 142, Issue 3
DOI: 10.1063/1.4905332

Exact stochastic simulation of coupled chemical reactions
journal, December 1977

Gillespie, Daniel T.
The Journal of Physical Chemistry, Vol. 81, Issue 25
DOI: 10.1021/j100540a008

Metamodelling with independent and dependent inputs
journal, June 2013

Zuniga, M. Munoz; Kucherenko, S.; Shah, N.
Computer Physics Communications, Vol. 184, Issue 6
DOI: 10.1016/j.cpc.2013.02.005

Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics
journal, December 2008

Gómez-Uribe, Carlos A.; Verghese, George C.; Tzafriri, Abraham R.
The Journal of Chemical Physics, Vol. 129, Issue 24
DOI: 10.1063/1.3050350

Multilevel Monte Carlo Path Simulation
journal, June 2008

Giles, Michael B.
Operations Research, Vol. 56, Issue 3
DOI: 10.1287/opre.1070.0496

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang
The Journal of Chemical Physics, Vol. 119, Issue 24
DOI: 10.1063/1.1627296

Dynamical Structures in Stochastic Chemical Reaction Systems
journal, January 2014

Han, Xiaoying; Najm, Habib N.
SIAM Journal on Applied Dynamical Systems, Vol. 13, Issue 3
DOI: 10.1137/140957482

Simplified CSP analysis of a stiff stochastic ODE system
journal, April 2012

Salloum, Maher; Alexanderian, Alen; Le Maître, Olivier P.
Computer Methods in Applied Mechanics and Engineering, Vol. 217-220
DOI: 10.1016/j.cma.2012.01.001

Global uncertainty assessments by high dimensional model representations (HDMR)
journal, November 2002

Li, Genyuan; Wang, Sheng-Wei; Rabitz, Herschel
Chemical Engineering Science, Vol. 57, Issue 21
DOI: 10.1016/S0009-2509(02)00417-7

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

Gillespie, Daniel T.
Journal of Computational Physics, Vol. 22, Issue 4
DOI: 10.1016/0021-9991(76)90041-3

Model reduction for slow–fast stochastic systems with metastable behaviour
journal, May 2014

Bruna, Maria; Chapman, S. Jonathan; Smith, Matthew J.
The Journal of Chemical Physics, Vol. 140, Issue 17
DOI: 10.1063/1.4871694

A modified next reaction method for simulating chemical systems with time dependent propensities and delays
journal, December 2007

Anderson, David F.
The Journal of Chemical Physics, Vol. 127, Issue 21
DOI: 10.1063/1.2799998

Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
journal, January 2007

E., Weinan; Liu, Di; Vanden-Eijnden, Eric
Journal of Computational Physics, Vol. 221, Issue 1
DOI: 10.1016/j.jcp.2006.06.019

Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
journal, February 2001

Sobol′, I. M.
Mathematics and Computers in Simulation, Vol. 55, Issue 1-3
DOI: 10.1016/S0378-4754(00)00270-6

Generalized Sobol sensitivity indices for dependent variables: numerical methods
journal, January 2014

Chastaing, G.; Gamboa, F.; Prieur, C.
Journal of Statistical Computation and Simulation, Vol. 85, Issue 7
DOI: 10.1080/00949655.2014.960415

Improved leap-size selection for accelerated stochastic simulation
journal, October 2003

Gillespie, Daniel T.; Petzold, Linda R.
The Journal of Chemical Physics, Vol. 119, Issue 16
DOI: 10.1063/1.1613254

Multilevel hybrid Chernoff tau-leap
journal, April 2015

Moraes, Alvaro; Tempone, Raúl; Vilanova, Pedro
BIT Numerical Mathematics, Vol. 56, Issue 1
DOI: 10.1007/s10543-015-0556-y

A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks
journal, December 2012

Wolf, Elizabeth Skubak; Anderson, David F.
The Journal of Chemical Physics, Vol. 137, Issue 22
DOI: 10.1063/1.4770052

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Title: Variance decomposition in stochastic simulators

Citation Formats

Polynomial chaos expansion for sensitivity analysis journal, July 2009

Bayesian Inference of Spectral Expansions for Predictability Assessment in Stochastic Reaction Networks journal, October 2009

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation journal, January 2012

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics journal, July 2013

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A Class of Statistics with Asymptotically Normal Distribution journal, September 1948

Hybrid Chernoff Tau-Leap journal, January 2014

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks journal, January 2010

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore journal, May 2013

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels journal, March 2000

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters journal, May 2013

A rigorous derivation of the chemical master equation journal, September 1992

Approximate accelerated stochastic simulation of chemically reacting systems journal, July 2001

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics journal, January 2012

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A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems journal, January 2012

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Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs journal, May 2010

PC analysis of stochastic differential equations driven by Wiener noise journal, March 2015

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems journal, January 2015

Exact stochastic simulation of coupled chemical reactions journal, December 1977

Metamodelling with independent and dependent inputs journal, June 2013

Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics journal, December 2008

Multilevel Monte Carlo Path Simulation journal, June 2008

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method journal, December 2003

Dynamical Structures in Stochastic Chemical Reaction Systems journal, January 2014

Simplified CSP analysis of a stiff stochastic ODE system journal, April 2012

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A general method for numerically simulating the stochastic time evolution of coupled chemical reactions journal, December 1976

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A modified next reaction method for simulating chemical systems with time dependent propensities and delays journal, December 2007

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Polynomial chaos expansion for sensitivity analysis
journal, July 2009

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journal, January 2012

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
journal, July 2013

Importance measures in global sensitivity analysis of nonlinear models
journal, April 1996

A Class of Statistics with Asymptotically Normal Distribution
journal, September 1948

Hybrid Chernoff Tau-Leap
journal, January 2014

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks
journal, January 2010

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore
journal, May 2013

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels
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journal, May 2013

A rigorous derivation of the chemical master equation
journal, September 1992

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journal, July 2001

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journal, January 2012

Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis
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Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters
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journal, March 2015

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems
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Exact stochastic simulation of coupled chemical reactions
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Metamodelling with independent and dependent inputs
journal, June 2013

Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics
journal, December 2008

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journal, June 2008

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

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journal, January 2014

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journal, April 2012

Global uncertainty assessments by high dimensional model representations (HDMR)
journal, November 2002

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
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journal, May 2014

A modified next reaction method for simulating chemical systems with time dependent propensities and delays
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journal, January 2007

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journal, February 2001

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journal, January 2014

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journal, October 2003

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journal, April 2015

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