1,103
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Bootstrapping least-squares estimates in biochemical reaction networks

&
Pages 125-146 | Received 27 Jun 2014, Accepted 18 Mar 2015, Published online: 22 Apr 2015

References

  • H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis, Vol. 4, Springer, New York, NY, 2000.
  • D.F. Anderson and T.G. Kurtz, Continuous Time Markov Chain Models for Chemical Reaction Networks, in Design and Analysis of Biomolecular Circuits, H. Koeppl, G. Setti, M. di Bernardo, and D. Densmore, eds., Springer, New York, NY, 2011, 3–42.
  • K. Ball, T.G. Kurtz, L. Popovic, and G. Rempala, Asymptotic analysis of multiscale approximations to reaction networks, Ann. Appl. Probab. 16(4) (2006), pp. 1925–1961. doi: 10.1214/105051606000000420
  • M.W. Chevalier and H. El-Samad, A data-integrated method for analyzing stochastic biochemical networks, J. Chem. Phys. 135(21) (2011), 214110. doi: 10.1063/1.3664126
  • A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the em algorithm, J. R. Statist. Soc. Ser. B (Methodol.) 39(1) (1977), pp. 1–38.
  • B. Efron and G. Gong, A leisurely look at the bootstrap, the jackknife, and cross-validation, Amer. Statist. 37(1) (1983), pp. 36–48.
  • S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, Vol. 282, Wiley, New York, NY, 2009.
  • D.T. Gillespie, A rigorous derivation of the chemical master equation, Phys. A: Statist. Mech. Appl. 188(1) (1992), pp. 404–425. doi: 10.1016/0378-4371(92)90283-V
  • A. Golightly and D.J. Wilkinson, Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo, Interface Focus 1(6) (2011), pp. 807–820. doi: 10.1098/rsfs.2011.0047
  • T. Hastie, R. Tibshirani, J. Friedman, T. Hastie, J. Friedman, and R. Tibshirani, The Elements of Statistical Learning, Vol. 2, Springer, New York, NY, 2009.
  • M. Komorowski, M.J. Costa, D.A. Rand, and M. P.H. Stumpf, Sensitivity, robustness, and identifiability in stochastic chemical kinetics models, Proc. Natl. Acad. Sci. USA 108(21) (2011), pp. 8645–8650. doi: 10.1073/pnas.1015814108
  • M. Komorowski, B. Finkenstädt, C.V. Harper, and D.A. Rand, Bayesian inference of biochemical kinetic parameters using the linear noise approximation, BMC Bioinformatics 10(1) (2009), p. 343. doi: 10.1186/1471-2105-10-343
  • J.R. Masters, Hela cells 50 years on: The good, the bad and the ugly, Nat. Rev. Cancer 2(4) (2002), pp. 315–319. doi: 10.1038/nrc775
  • G.J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, Vol. 382, Wiley-Interscience, New York, NY, 2007.
  • O.D. Perez, P.O. Krutzik, and G.P. Nolan, Flow cytometric analysis of kinase signaling cascades, Methods Mol. Biol. 263(2004), pp. 67–94.
  • G.A. Rempala, Least squares estimation in stochastic biochemical networks, Bull. Math. Biol. 74(8) (2012), pp. 1938–1955. doi: 10.1007/s11538-012-9744-y
  • G.A. Rempala, K.S. Ramos, and T. Kalbfleisch, A stochastic model of gene transcription: an application to l1 retrotransposition events, J. Theoret. Biol. 242(1) (2006), pp. 101–116. doi: 10.1016/j.jtbi.2006.02.010
  • G.A. Rempala, K.S. Ramos, T. Kalbfleisch, and I. Teneng, Validation of a mathematical model of gene transcription in aggregated cellular systems: application to l1 retrotransposition, J. Comput. Biol. 14(3) (2007), pp. 339–349. doi: 10.1089/cmb.2006.0125
  • A. Roberts, C. Trapnell, J. Donaghey, J.L. Rinn, and L. Pachter, Improving RNA-Seq expression estimates by correcting for fragment bias, Genome Biol. 12(3) (2011), p. R22. doi: 10.1186/gb-2011-12-3-r22
  • A. Ruszczynski, Nonlinear Optimization, Vol. 13, Princeton University Press, Princeton, NJ, 2011.
  • L. Salwinski and D. Eisenberg, In silico simulation of biological network dynamics, Nat. Biotechnol. 22(8) (2004), pp. 1017–1019. doi: 10.1038/nbt991
  • J. Shao, Mathematical Statistics, 2nd ed., Springer, New York, NY, 2003.
  • R. Tibshirani, Regression shrinkage and selection via the lasso: a retrospective, J. R. Statist. Soc: Ser. B (Statist. Methodol.) 73(3) (2011), pp. 273–282. doi: 10.1111/j.1467-9868.2011.00771.x
  • N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Vol. 1, Elsevier North-Holland, Amsterdam, 1992.
  • M.D. Wang, M.J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S.M. Block, Force and velocity measured for single molecules of RNA polymerase, Science 282(5390) (1998), pp. 902–907. doi: 10.1126/science.282.5390.902
  • D.A. Wheeler, M. Srinivasan, M. Egholm, Y. Shen, L. Chen, A. McGuire, W. He, Y.-J. Chen, V. Makhijani, G.T. Roth, X. Gomes, K. Tartaro, F. Niazi, C.L. Turcotte, G.P. Irzyk, J.R. Lupski, C. Chinault, X.-z. Song, Y. Liu, Y. Yuan, L. Nazareth, X. Qin, D.M. Muzny, M. Margulies, G.M. Weinstock, R.A. Gibbs, and J.M. Rothberg, The complete genome of an individual by massively parallel DNA sequencing, Nature 452(7189) (2008), pp. 872–876. doi: 10.1038/nature06884
  • D.J. Wilkinson, Stochastic modelling for quantitative description of heterogeneous biological systems, Nat. Rev. Genet. 10(2) (2009), pp. 122–133. doi: 10.1038/nrg2509
  • D.J. Wilkinson, Stochastic Modelling for Systems Biology, Vol. 44, CRC Press, Boca Raton, FL, 2011.
  • H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Statist. Soc: Ser. B (Statist. Methodol.) 67(2) (2005), pp. 301–320. doi: 10.1111/j.1467-9868.2005.00503.x