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Bayesian Abstraction of Markov Population Models

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Quantitative Evaluation of Systems (QEST 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11785))

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Markov Population Models are a widespread formalism, with applications in Systems Biology, Performance Evaluation, Ecology, and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when simulations have to be performed in a multi-scale model (e.g. simulating individual cells in a tissue). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous work [3] and constructing an approximate kernel for a Markov process in continuous space and discrete time, capturing the evolution at fixed \(\varDelta t\) time steps. This kernel is learned automatically from simulations of the original model. Differently from [3], which relies on deep neural networks, we explore here a Bayesian density regression approach based on Dirichlet processes, which provides a principled way to estimate uncertainty.

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  1. Barber, D.: Bayesian Reasoning and Machine Learning. Cambridge University Press, Cambridge (2012)

    MATH  Google Scholar 

  2. Bodei, C., Bortolussi, L., Chiarugi, D., Guerriero, M.L., Policriti, A., Romanel, A.: On the impact of discreteness and abstractions on modellingnoise in gene regulatory networks. Comput. Biol. Chem. 56, 98–108 (2015)

    Article  Google Scholar 

  3. Bortolussi, L., Palmieri, L.: Deep abstractions of chemical reaction networks. In: Češka, M., Šafránek, D. (eds.) CMSB 2018. LNCS, vol. 11095, pp. 21–38. Springer, Cham (2018).

    Chapter  Google Scholar 

  4. Cao, Y., Petzold, L.: Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems. J. Comput. Phys. 212(1), 6–24 (2006)

    Article  MathSciNet  Google Scholar 

  5. Deisboeck, T.S., Wang, Z., Macklin, P., Cristini, V.: Multiscale cancer modeling. Annu. Rev. Biomed. Eng. 13(1), 127–155 (2011).

    Article  Google Scholar 

  6. Dunson, D.B.: Empirical bayes density regression. Statistica Sinica 17(2), 481 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Dunson, D.B., Pillai, N., Park, J.H.: Bayesian density regression. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 69(2), 163–183 (2007)

    Article  MathSciNet  Google Scholar 

  8. Ferguson, T.S.: A bayesian analysis of some nonparametric problems. Ann. Stat. 1, 209–230 (1973)

    Article  MathSciNet  Google Scholar 

  9. Gelman, A., Stern, H.S., Carlin, J.B., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC, Boca Raton (2013)

    MATH  Google Scholar 

  10. Gillespie, D.T., Petzold, L.: Numerical simulation for biochemical kinetics. In: Szallasi, Z., Stelling, J., Periwal, V. (eds.) Systems Modelling in Cellular Biology, pp. 331–354. MIT Press, Cambridge (2006)

    Chapter  Google Scholar 

  11. Ishwaran, H., James, L.F.: Gibbs sampling methods for stick-breaking priors. J. Am. Stat. Assoc. 96(453), 161–173 (2001)

    Article  MathSciNet  Google Scholar 

  12. Maarleveld, T.R., Olivier, B.G., Bruggeman, F.J.: Stochpy: a comprehensive, user-friendly tool for simulating stochastic biological processes. PLoS ONE 8(11), e79345 (2013)

    Article  Google Scholar 

  13. Michaelides, M., Hillston, J., Sanguinetti, G.: Statistical abstraction for multi-scale spatio-temporal systems. In: Bertrand, N., Bortolussi, L. (eds.) QEST 2017. LNCS, vol. 10503, pp. 243–258. Springer, Cham (2017).

    Chapter  Google Scholar 

  14. Norris, J.R.: Markov Chains. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  15. Nott, D.J., Tan, S.L., Villani, M., Kohn, R.: Regression density estimation with variational methods and stochastic approximation. J. Comput. Graph. Stat. 21(3), 797–820 (2012)

    Article  MathSciNet  Google Scholar 

  16. Palaniappan, S.K., Bertaux, F., Pichené, M., Fabre, E., Batt, G., Genest, B.: Abstracting the dynamics of biological pathways using information theory. Bioinformatics 33, 1980–1986 (2017)

    Article  Google Scholar 

  17. Sethuraman, J.: A constructive definition of dirichlet priors. Statistica Sinica 4, 639–650 (1994)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Francesca Cairoli .

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Bortolussi, L., Cairoli, F. (2019). Bayesian Abstraction of Markov Population Models. In: Parker, D., Wolf, V. (eds) Quantitative Evaluation of Systems. QEST 2019. Lecture Notes in Computer Science(), vol 11785. Springer, Cham.

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  • Print ISBN: 978-3-030-30280-1

  • Online ISBN: 978-3-030-30281-8

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