The Importance and Challenges of Bayesian Parameter Learning in Systems Biology

  • Johanna Mazur
  • Lars Kaderali
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 4)


In the last decade a new research field has emerged: Systems Biology. Based on experimental data and using mathematical and computational methods, systems biology attempts to describe biological behavior in a quantitative dynamic way. Biological data contains a lot of noise and there is only a limited amount available due to high experimental effort and cost. Thus, for parameter estimation from this kind of data, their stochasticity and the problem of non-identifiability of model parameters has to be taken into account. One way to do this is using a Bayesian framework, where one obtains distributions over possible parameter values, and these are then further analyzed. In this article we describe the potential impact of Bayesian parameter learning on systems biology, and discuss challenges arising from a Bayesian approach.


Posterior Distribution Markov Chain Monte Carlo System Biology Markov Chain Monte Carlo Algorithm Parameter Estimation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are grateful for funding to the German Ministry of Education and Research (BMBF), grant number 0313923 (FORSYS/Viroquant).


  1. 1.
    C. Andrieu and J. Thoms. A tutorial on adaptive MCMC. Stat. Comput., 18:343–373, 2008.MathSciNetCrossRefGoogle Scholar
  2. 2.
    S. Bandara, J. P. Schlöder, R. Eils, H. G. Bock, and T. Meyer. Optimal experimental design for parameter estimation of a cell signaling model. PLoS Comput. Biol., 5(11):e1000558, 2009.Google Scholar
  3. 3.
    R. J. Boys, D. J. Wilkinson, and T. B. L. Kirkwood. Bayesian inference for a discretely observed stochastic kinetic model. Stat. Comput., 18(2):125–135, 2008.MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. G. Busetto, C. S. Ong, and J. M. Buhmann. Optimized expected information gain for nonlinear dynamical systems. In A. P. Danyluk, L. Bottou, and M. L. Littman, editors, ICML, volume 382 of ACM International Conference Proceeding Series, page 13. ACM, 2009.Google Scholar
  5. 5.
    K. Chaloner and I. Verdinelli. Bayesian experimental design: A review. Statist. Sci., 10(3):273–304, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    D. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Hybrid Monte Carlo. Phys. Lett. B, 195:216–222, 1987.CrossRefGoogle Scholar
  7. 7.
    M. Girolami. Bayesian inference for differential equations. Theor. Comp. Sci., 408:4–16, 2008.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    P. Gustafson. What are the limits of posterior distributions arising from nonidentified models, and why should we care? J. Am. Stat. Assoc., 104(488):1682–1695, 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    R. N. Gutenkunst, J. J. Waterfall, F. P. Casey, K. S. Brown, C. R. Myers, and J. P. Sethna. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol., 3(10):e189, 2007.Google Scholar
  10. 10.
    W. K. Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1):97–109, 1970.zbMATHCrossRefGoogle Scholar
  11. 11.
    A. Jasra, D. A. Stephens, and C. C. Holmes. On population-based simulation for static inference. Stat. Comput., 17:263–279, 2007.MathSciNetCrossRefGoogle Scholar
  12. 12.
    L. Kaderali and N. Radde. Inferring gene regulatory networks from expression data. In A. Kelemen, A. Abraham, and Y. Chen, editors, Computational Intelligence in Bioinformatics, volume 94 of Studies in Computational Intelligence, pages 33–74. Springer, Berlin, 2008.CrossRefGoogle Scholar
  13. 13.
    G. Karlebach and R. Shamir. Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol., 9:770–780, 2008.CrossRefGoogle Scholar
  14. 14.
    J. Kiefer. Optimum experimental designs. J. R. Stat. Soc. Series B Methodol., 21(2):272–319, 1959.MathSciNetzbMATHGoogle Scholar
  15. 15.
    C. Kreutz and J. Timmer. Systems biology: experimental design. FEBS J., 276:923–942, 2009.CrossRefGoogle Scholar
  16. 16.
    J. Mazur, D. Ritter, G. Reinelt, and L. Kaderali. Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling. BMC Bioinformatics, 10:448, 2009.CrossRefGoogle Scholar
  17. 17.
    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller. Equations of state calculations by fast computing machines. J. Chem. Phys., 21(6):1087–1092, 1953.CrossRefGoogle Scholar
  18. 18.
    R. M. Neal. Probabilistic inference using Markov chain Monte Carlo methods. Technical report, Department of Computer Science, University of Toronto, 1993.Google Scholar
  19. 19.
    A. O’Hagan and J. F. C. Kingman. Curve fitting and optimal design for prediction. J. R. Stat. Soc. Series B Methodol., 40(1):1–42, 1978.zbMATHGoogle Scholar
  20. 20.
    M. C. Shewry and H. P. Wynn. Maximum entropy sampling. J. Appl. Stat., 14(2):165–170, 1987.CrossRefGoogle Scholar
  21. 21.
    F. Steinke, M. Seeger, and K. Tsuda. Experimental design for efficient identification of gene regulatory networks using sparse Bayesian models. BMC Syst. Biol., 1:51, 2007.CrossRefGoogle Scholar
  22. 22.
    J. van den Berg, A. Curtis, and J. Trampert. Optimal nonlinear Bayesian experimental design: an application to amplitude versus offset experiments. Geophys. J. Int., 155(2):411–421, 2003.CrossRefGoogle Scholar
  23. 23.
    V. Vyshemirsky and M. Girolami. Bayesian ranking of biochemical system models. Bioinformatics, 24(6):833–839, 2008.CrossRefGoogle Scholar
  24. 24.
    V. Vyshemirsky and M. Girolami. BioBayes: A software package for Bayesian inference in systems biology. Bioinformatics, 24(17):1933–1934, 2008.CrossRefGoogle Scholar
  25. 25.
    D. J. Wilkinson. Stochastic Modelling for Systems Biology. Chapman & Hall/CRC, Boca Raton, FL, USA, 2006.zbMATHGoogle Scholar
  26. 26.
    D. J. Wilkinson. Stochastic modelling for quantitative description of heterogeneous biological systems. Nat. Rev. Genet., 10:122–133, 2009.CrossRefGoogle Scholar
  27. 27.
    Y. Xie and B. P. Carlin. Measures of Bayesian learning and identifiability in hierarchical models. J. Stat. Plan. Inference, 136:3458–3477, 2006.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Viroquant Research Group ModelingUniversity of HeidelbergHeidelbergGermany

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