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Journal of Nonlinear Science

, Volume 28, Issue 1, pp 371–393 | Cite as

The Stochastic Quasi-chemical Model for Bacterial Growth: Variational Bayesian Parameter Update

  • Panagiotis Tsilifis
  • William J. Browning
  • Thomas E. Wood
  • Paul K. Newton
  • Roger G. Ghanem
Article
  • 246 Downloads

Abstract

We develop Bayesian methodologies for constructing and estimating a stochastic quasi-chemical model (QCM) for bacterial growth. The deterministic QCM, described as a nonlinear system of ODEs, is treated as a dynamical system with random parameters, and a variational approach is used to approximate their probability distributions and explore the propagation of uncertainty through the model. The approach consists of approximating the parameters’ posterior distribution by a probability measure chosen from a parametric family, through minimization of their Kullback–Leibler divergence.

Keywords

Bayes rule Kullback–Leibler divergence Evidence lower bound Quasi-chemical model Gradient-based optimization 

Notes

Acknowledgements

The authors gratefully acknowledge support from US Army Research Office Contract W911NF-14-C-0151.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Panagiotis Tsilifis
    • 1
  • William J. Browning
    • 2
  • Thomas E. Wood
    • 2
  • Paul K. Newton
    • 3
  • Roger G. Ghanem
    • 1
  1. 1.Department of Civil EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Applied Mathematics Inc.Gales FerryUSA
  3. 3.Department of Aerospace and Mechanical Engineering and MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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