Bayesian inference for a discretely observed stochastic kinetic model

Statistics and Computing

Volumn 18, Issue 2, 2008, Pages 125-135

  Boys, R J ^a   Wilkinson, D J ^a   Kirkwood, T B L ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Biochemical networks; Block updating; Lotka Volterra model; Markov jump process; MCMC methods; Parameter estimation; Reversible jump; Systems biology

Indexed keywords

EID: 41549140160     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-007-9043-x     Document Type: Article

References (38)

1. Abramowitz, M., Stegun, I.A. (eds.): Pocketbook of Mathematical Functions. Harri Deutsch, Frankfurt (1984), Chap. 9.6
2. Arkin, A., Ross, J., McAdams, H.H.: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149, 633-648 (1998)
3. Bahcall, O.G.: Single cell resolution in regulation of gene expression, Mol. Syst. Biol. (2005). doi: 10.1038/msb4100020
4. Barenco, M., Tomescu, D., Brewer, D., Callard, R., Stark, J., Hubank, M.: Ranked prediction of p53 targets using hidden variable dynamic modeling. Genome Biol. 7, R25 (2006)
5. Blackwell, P.G.: Bayesian inference for Markov processes with diffusion and discrete components. Biometrika 90, 613-627 (2003)
6. Bower, J.M., Bolouri, H. (eds.): Computational Modeling of Genetic and Biochemical Networks. MIT Press, Cambridge (2001)
7. Boys, R.J., Giles, P.R.: Bayesian inference for SEIR epidemic models with time-inhomogeneous removal rates. J. Math. Biol. 55, 223-247 (2007)
8. Brown, K.S., Sethna, J.P.: Statistical mechanical approaches to models with many poorly known parameters. Phys. Rev. E 68, 021904 (2003)
9. Carter, C.K., Kohn, R.: Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika 83, 589-601 (1996)
10. Finch, C.E., Kirkwood, T.B.L.: Chance, Development and Aging. Oxford University Press, New York (2000)
11. Gibson, G.J., Renshaw, E.: Estimating parameters in stochastic compartmental models using Markov chain methods. IMA J. Math. Appl. Med. Biol. 15, 19-40 (1998)
12. Gilioli, G., Pasquali, S., Ruggeri, F.: Bayesian inference for functional response in a stochastic predator-prey system. IBull. Math. Biol. (2008). doi: 10.1007/s11538-007-9256-3
13. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340-2361 (1977)
14. Golightly, A., Wilkinson, D.J.: Bayesian sequential inference for stochastic kinetic biochemical network models. J. Comput. Biol. 13(3), 838-851 (2006)
15. Golightly, A., Wilkinson, D.J.: Bayesian inference for nonlinear multivariate diffusion models observed with error. Comput. Stat. Data Anal. 52, 1674-1693 (2008)
16. Green, P.J.: Trans-dimensional Markov chain Monte Carlo. In: Green, P.J., Hjørt, N.L., Richardson, S. (eds.) Highly Structured Stochastic Systems, pp. 179-198. Oxford University Press, Oxford (2003)
17. Guptasarma, P.: Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli? BioEssays 17, 987-997 (1995)
18. Johnson, N.L., Kotz, S.: Discrete distributions. In: Distributions in Statistics, vol. 1, p. 115. Wiley, New York (1969)
19. Jost, C., Arditi, R.: Identifying predator-prey processes from time-series. Theor. Pop. Biol. 57, 325-337 (2000)
20. Kirkwood, T.B.L., Boys, R.J., Gillespie, C.S., Proctor, C.J., Shanley, D.P., Wilkinson, D.J.: Towards an e-biology of ageing: integrating theory and data. Nat. Rev. Mol. Cell Biol. 4, 243-249 (2003)
21. Kitano, H. (ed.): Foundations of Systems Biology. MIT Press, Cambridge (2001)
22. Liebermeister, W., Klipp, E.: Biochemical networks with uncertain parameters. IEE Syst. Biol. 152(3), 97-107 (2005)
23. Liechty, J.C., Roberts, G.O.: Markov chain Monte Carlo methods for switching diffusion models. Biometrika 88, 299-315 (2001)
24. Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925)
25. McAdams, H.H., Arkin, A.: Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94, 814-819 (1997)
26. McAdams, H.H., Arkin, A.: It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15, 65-69 (1999)
27. Pepperkok, R., Ellenberg, J.: High-throughput fluorescence microscopy for systems biology. Nat. Rev. Mol. Cell Biol. 7, 690-696 (2006)
28. Reinker, S., Altman, R.M., Timmer, J.: Parameter estimation in stochastic biochemical reactions. IEE Syst. Biol. 153(4), 168-178 (2006)
29. Rempala, G.A., Ramos, K.S., Kalbfleisch, T.: A stochastic model of gene transcription: an application to L1 retrotransposition events. J. Theor. Biol. 242(1), 101-116 (2006)
30. Renshaw, E.: Modelling Biological Populations in Space and Time. Cambridge University Press, Cambridge (1991)
31. Shen, H., Nelson, G., Nelson, D.E., Kennedy, S., Spiller, D.G., Griffiths, T., Paton, N., Oliver, S.G., White, M.R.H., Kell, D.B.: Automated tracking of gene expression profiles in individual cells and cell compartments. J. R. Soc. Interface 3, 787-794 (2006)
32. Shephard, N., Pitt, M.K.: Likelihood analysis of non-Gaussian measurement time series. Biometrika 84(3), 653-667 (1997)
33. Tian, T., Xu, S., Gao, J., Burrage, K.: Simulated maximum likelihood method for estimating kinetic rates in gene expression. Bioinformatics 23, 84-91 (2007)
34. Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560 (1926)
35. Wilkinson, D.J.: Stochastic Modelling for Systems Biology. Chapman & Hall/CRC, Boca Raton (2006)
36. Wilkinson, D.J., Yeung, S.K.H.: A sparse matrix approach to Bayesian computation in large linear models. Comput. Stat. Data Anal. 44, 493-516 (2004)
37. Zheng, Q., Ross, J.: Comparison of deterministic and stochastic kinetics for nonlinear systems. J. Chem. Phys. 94, 3644-3648 (1991)
38. Zlokarnik, G., Negulescu, P.A., Knapp, T.E., Mere, L., Burres, N., Feng, L., Whitney, M., Roemer, K., Tsien, R.Y.: Quantitation of transcription and clonal selection of single living cells with β-lactamase as reporter. Science 279, 84-88 (1998)