Rate estimation in partially observed Markov jump processes with measurement errors

Statistics and Computing

Volumn 22, Issue 2, 2012, Pages 513-526

  Amrein, Michael ^a   Künsch, Hans R ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Bayesian inference; General state space model; Markov chain Monte Carlo methods; Markov jump process; Particle filter; Stochastic kinetics

Indexed keywords

EID: 81955160894     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-011-9244-1     Document Type: Article

References (26)

1. Arkin, A., Ross, J., McAdams, H. H.: Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected escherichia coli cells. Genetics 149, 1633-1648 (1998).
2. Bickel, P. J., Doksum, K. A.: Mathematical Statistics; Basic Ideas and Selected Topics. Holden-Day Inc., Oakland (1977).
3. Boys, R. J., Wilkinson, D. J., Kirkwood, T. B.: Bayesian inference for a discretely observed stochastic kinetic model. Stat. Comput. 18(2), 125-135 (2008).
4. Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Berlin (1993).
5. Doucet, A., de Freitas, J. F. G., Gordon, N. J.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001).
6. Durham, G., Gallant, R.: Numerical techniques for maximum likelihood estimation of continuous time diffusion processes. J. Bus. Econ. Stat. 20, 279-316 (2002).
7. Fearnhead, P., Meligkotsidou, L.: Exact filtering for partially observed continuous time models. J. R. Stat. Soc. B 66(3), 771-789 (2004).
8. Gibson, M. A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104(9), 1876-1889 (2000).
9. Gilks, W. R., Berzuini, C.: Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. R. Stat. Soc. B 63(1), 127-146 (2001).
10. Gilks, W. R., Richardson, S., Spiegelhalter, D. J.: Markov Chain Monte Carlo in Practice. Chapman and Hall, London (1996).
11. Gillespie, D. T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340-2360 (1977).
12. Golightly, A., Wilkinson, D.: Bayesian inference for nonlinear multivariate diffusion models observed with error. Comput. Stat. Data Anal. 52(3), 1674-1693 (2008).
13. Golightly, A., Wilkinson, D. J.: Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics 61, 781-788 (2005).
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.: Markov chain Monte Carlo algorithms for SDE parameter estimation. In: Learning and Inference for Computational Systems Biology. MIT Press, Cambridge (2009).
16. Hobolth, A., Stone, EA: Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution. Ann. Appl. Stat. 3(3), 1204-1231 (2009).
17. Jäger, G.: Algorithmen zur Berechnung der Smith-Normalform und deren Implementation auf Parallelrechnern. PhD thesis, Universität Essen, Fachbereich 6 (Mathematik und Informatik) (2001).
18. Künsch, H. R.: Complex Stochastic Systems. Chapman & Hall/CRC, London (2000), Chap. 3.
19. McAdams, H., Arkin, A.: Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94, 814-819 (1997).
20. Newman, M.: Integral Matrices. Academic Press, New York (1972).
21. Ogata, Y.: On Lewis' simulation method for point processes. IEEE Trans. Inf. Theory 27(1), 23-31 (1981).
22. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2010). http://www. R-project. org.
23. Ripley, B. D.: Stochastic Simulation. Wiley, New York (1987).
24. Robert, C. P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer Texts in Statistics. Springer, New York (2004).
25. Storjohann, A., Labahn, G.: Asymptotically fast computation of Hermite normal forms of integer matrices. In: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, ISSAC '96, pp. 259-266. ACM, New York (1996).
26. Wilkinson, D. J.: Stochastic Modelling for Systems Biology. Chapman & Hall, London (2006).