Other Stochastic Methods and Prism



This chapter introduces the reader to the concept of stochastic systems. It motivates the importance of noise and stochastic fluctuations in biological modeling and introduces some of the basic concepts of stochastic systems, including Markov chains and partition functions. The main objective of this theoretical part is to provide the reader with sufficient theoretical background to be able to understand original research papers in the field. Strong emphasis is placed on conveying a conceptual understanding of the topics, while avoiding burdening the reader with unnecessary mathematical detail. The second part of this chapter describes PRISM, which is a powerful computational tool for formulating, analyzing and simulating Markov-chain models. Throughout the chapter, concepts are illustrated using biologically-motivated case studies.


Markov Chain Partition Function Model Check Transition Matrix Master Equation 
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  1. 8.
    Cherry, J., Adler, F.: How to make a biological switch. Journal of Theoretical Biology 203(2), 117–133 (2000). doi: 10.1006/jtbi.2000.1068 CrossRefGoogle Scholar
  2. 10.
    Chu, D., Zabet, N., Mitavskiy, B.: Models of transcription factor binding: sensitivity of activation functions to model assumptions. Journal of Theoretical Biology 257(3), 419–429 (2009). doi: 10.1016/j.jtbi.2008.11.026 CrossRefGoogle Scholar
  3. 18.
    Gardiner, C.: Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences. Springer, Berlin (2008) Google Scholar
  4. 29.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Kemper, P. (ed.) Proc. Tools Session of Aachen 2001 International Multiconference on Measurement, Moddeling and Evaluation of Computer-Communication Systems, pp. 7–12, September 2001 Google Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Computing LaboratoryUniversity of KentCanterbury, KentUK

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