Fast integration-based prediction bands for ordinary differential equation models

Bioinformatics

Volumn 32, Issue 8, 2016, Pages 1204-1210

  Hass, Helge ^a   Kreutz, Clemens ^a   Timmer, Jens ^a   Kaschek, Daniel ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MODEL; METHODOLOGY; NONLINEAR SYSTEM; PROBABILITY; UNCERTAINTY;

MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PROBABILITY; RESEARCH DESIGN; UNCERTAINTY;

EID: 84966632715     PISSN: 13674803     EISSN: 14602059     Source Type: Journal    
DOI: 10.1093/bioinformatics/btv743     Document Type: Article

References (32)

1. Bachmann, J. et al. (2011) Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range. Mol. Syst. Biol., 7, 516.
2. Bjornstad, J.F. (1990) Predictive likelihood: a review. Stat. Sci., 5, 242-254.
3. Butcher, J.C. (1963) Coefficients for the study of runge-kutta integration processes. J. Aust. Math. Soc., 3, 185-201.
4. Chen, J.S., Jennrich, R.I. (2002) Simple accurate approximation of likelihood profiles. J. Comput. Graph. Stat., 11, 714-732.
5. De Boor, C. (1978). A Practical Guide to Splines, Vol. 27. Springer, New York.
6. Feder, P.I. (1968) On the distribution of the log likelihood ratio test statistic when the true parameter is "near" the boundaries of the hypothesis regions. Ann. Math. Stat., 39, 2044-2055.
7. Fisher, R.A. (1912) On an absolute criterion for fitting frequency curves. Messenger Math., 41, 155-160.
8. Floares, A.G., Luludachi, I. (2014). Inferring transcription networks from data. In: Kasabov, N. (ed), Springer Handbook of Bio-/Neuroinformatics, Springer Science and Business Media, pp. 311-326.
9. Gilks, W.R. (2005). Markov Chain Monte Carlo. Wiley Online Library.
10. Griewank, A., Walther, A. (2008). Evaluating derivatives: principles and techniques of algorithmic differentiation. SIAM J. Sci. Comput. 32, 3323-3351.
11. Hahn, G.J., Nelson, W. (1973) A survey of prediction intervals and their applications. J. Qual. Technol., 5, 178-188.
12. Hecker, M. et al. (2009) Gene regulatory network inference: data integration in dynamic models-a review. Biosystems, 96, 86-103.
13. Hinkley, D. (1979) Predictive likelihood. Ann. Stat., 7, 718-728.
14. Karlebach, G., Shamir, R. (2008) Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol., 9, 770-780.
15. Kreutz, C. et al. (2012) Likelihood based observability analysis and confidence intervals for predictions of dynamic models. BMC Syst. Biol., 6, 120.
16. Krishnan, A. et al. (2007) Indeterminacy of reverse engineering of gene regulatory networks: the curse of gene elasticity. PLoS One, 2, e562.
17. Merkt, B. et al. (2015) Higher-order lie-symmetries in identifiability and predictability analysis of dynamic models. Phys. Rev. E, 92, 12-20.
18. Neale, M.C., Miller, M.B. (1997) The use of likelihood-based confidence intervals in genetic models. Behav. Genet., 27, 113-120.
19. Nocedal, J., Wright, S. (2006). Numerical Optimization. Springer Science & Business Media, New York.
20. Powell, M.J. (1970) A new algorithm for unconstrained optimization. In: Rosen, J.B. et al (eds). Nonlinear Program, Academic Press, New York, pp. 31-65.
21. Press, W.H. et al. (1996). Numerical Recipes in C. Cambridge University Press, Cambridge.
22. Raia, V. et al. (2011) Dynamic mathematical modeling of IL13-induced signaling in Hodgkin and primary mediastinal B-cell lymphoma allows prediction of therapeutic targets. Cancer Res., 71, 693-704.
23. Raue, A. et al. (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics, 25, 1923-1929.
24. Raue, A. et al. (2013) Lessons learned from quantitative dynamical modeling in systems biology. PloS One, 8, e74335.
25. Raue, A. et al. (2015) Data2dynamics: a modeling environment tailored to parameter estimation in dynamical systems. Bioinformatics, 31, 3558-3560.
26. Sachs, L. (1984). Applied Statistics. Springer, New York.
27. Sakamoto, E., Iba, H. (2001). Inferring a system of differential equations for a gene regulatory network by using genetic programming. In Proceedings of the 2001 Congress on Evolutionary Computation, volume 1, pp. 720-726. IEEE.
28. Scott, D.W. (2009). Multivariate Density Estimation: Theory, Practice, and Visualization. John Wiley & Sons, New York.
29. Spieth, C. et al. (2006). Comparing mathematical models on the problem of network inference. In Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 279-286. ACM.
30. Swameye, I. et al. (2003) Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. Proc. Natl Acad. Sci. USA, 100, 1028-1033.
31. Venzon, D., Moolgavkar, S. (1988) A method for computing profile-likelihood-based confidence intervals. Appl. Stat., 37, 87-94.
32. Zhang, B.T., Mü hlenbein, H. (1995) Balancing accuracy and parsimony in genetic programming. Evol. Comput., 3, 17-38.