Preconditioned Bayesian regression for stochastic chemical kinetics

Alen Alexanderian, Francesco Rizzi, Muruhan Rathinam, Olivier P. Le Maître, Omar M. Knio*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis-Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.

Original languageEnglish (US)
Pages (from-to)592-626
Number of pages35
JournalJournal of Scientific Computing
Issue number3
StatePublished - Mar 2014

Bibliographical note

Funding Information:
Acknowledgments This work was supported by the US Department of Energy (DOE) under Award Numbers DE-SC0001980 and DE-SC0008789. The work of OLM is partially supported by the French Agence Nationale pour la Recherche (Project ANR-2010-Blan-0904) and the GNR MoMaS funded by Andra, Brgm, Cea, Edf, and Irsn. Finally, would like to thank the reviewer for helpful comments on improving this manuscript.


  • Bayesian regression
  • Chemical kinetics
  • Polynomial chaos
  • Preconditioner
  • Stochastic simulation algorithm

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • Numerical Analysis
  • Computational Theory and Mathematics


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