Bayesian system identification via Markov chain Monte Carlo techniques

Automatica

Volumn 46, Issue 1, 2010, Pages 40-51

  Ninness, Brett ^a   Henriksen, Soren ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Bayesian methods; Maximum likelihood; Parameter estimation; System identification

Indexed keywords

ARBITRARY FUNCTIONS; BAYESIAN; BAYESIAN APPROACHES; BAYESIAN METHODS; DATA RECORDS; DYNAMIC SYSTEMS; ERGODICS; ESTIMATION ERRORS; INVARIANT DENSITIES; MARKOV CHAIN; MARKOV CHAIN MONTE CARLO TECHNIQUES; METROPOLIS-HASTINGS ALGORITHM; MODEL PARAMETERS; MONTE CARLO ANALYSIS; SYSTEM IDENTIFICATIONS;

BAYESIAN NETWORKS; DYNAMICAL SYSTEMS; MARKOV PROCESSES; METAL ANALYSIS; MONTE CARLO METHODS; NUMERICAL METHODS; PARAMETER ESTIMATION;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 73049086204     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.10.015     Document Type: Article

References (39)

1. A °ström K. Maximum likelihood and prediction error methods. Automatica 16 (1980) 551-574
2. Bittanti S., and Lovera M. Bootstrap-based estimates of uncertainty in subspace identification methods. Automatica. A Journal of IFAC 36 (2000) 1605-1615
3. Caines P. Linear stochastic systems (1988), John Wiley and Sons, New York
4. Campi M.C., and Kumar P.R. Learning dynamical systems in a stationary environment. Systems and Control Letters 34 (1998) 125-132 Learning theory
5. Campi M.C., and Vidyasagar M. Learning with prior information. IEEE Transactions on Automatic Control 46 (2001) 1682-1695
6. Campi M.C., and Weyer E. Guaranteed non-asymptotic confidence regions in system identification. Automatica 41 (2005) 1751-1764
7. Douma, S. G., & Van den Hof, P. M. J. (2006). Probabilistic model uncertainty bounding: An approach with finite-time perspectives. In Preprints of the 14th IFAC Symposium on System Identification (pp. 1021-1026)
8. Dunstan, W.J., & Bitmead, R.R. (2003). Empirical estimation of parameter distributions in system identification. In Proceedings of the 13th IFAC Symposium on System Identification, The Netherlands
9. Efron B. Bayesians, frequentists and scientists. The American Statistician (2004). http://www-stat.stanford.edu/brad/papers/ Assoc. Presidential Address. Available electronically via http://www-stat.stanford.edu/brad/papers/
10. Efron B., and Tibshirani R. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science 1 (1986) 54-77 With a comment by J. A. Hartigan and a rejoinder by the authors
11. Garatti S., Campi M.C., and Bittanti S. Assessing the quality of identified models through the asymptotic theory-when is the result reliable?. Automatica. A Journal of IFAC 40 (2004) 1319-1332
12. Gilks W., Richardson S., and Spiegelhalter D. Markov Chain Monte Carlo in practice (1996), Chapman and Hall
13. Hastings W. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970) 97-109
14. The top ten algorithms - The Metropolis algorithm. In: Dongarra J. (Ed). Computing in Science and Engineering 2 (2000) 65-69
15. Jeffrey R. Subjective probability: The real thing (2004), Cambridge University Press
16. Jones G.L., and Hobert J.P. Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statistical Science 16 (2001) 312-334
17. Juloski A.L., Weiland S., and Heemels W.P.M.H. A Bayesian approach to identification of hybrid systems. IEEE Transactions on Automatic Control 50 (2005) 1520-1533
18. Lehmann E. Theory of point estimation (1983), John Wiley & Sons
19. Lindley D. Bayesian statistics: A review (1971), Society for Industrial and Applied Mathematics (SIAM), Philadelphia
20. Ljung L. System identification: Theory for the user. 2nd ed. (1999), Prentice-Hall, Inc, New Jersey
21. Ljung, L. (2004). MATLAB System Identification Toolbox Users Guide, Version 6, The Mathworks
22. Metropolis M., Rosenbluth A., Rosenbluth M., Teller A., and Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics 21 (1953) 1087-1091
23. Meyn S.P., and Tweedie R.L. Markov chains and stochastic stability (1993), Springer-Verlag, London
24. Milanese M., and Vicino A. Optimal inner bounds of feasible parameter set in linear estimation with bounded noise. IEEE Transactions on Automatic Control 36 (1991) 759
25. Ninness B. Strong laws of large numbers under weak assumptions with application. IEEE Transactions on Automatic Control 45 (2000) 2117-2122
26. Ninness, B., & Henriksen, S. (2003). A computational Bayesian approach to system identification. In Proceedings 13th IFAC Symposium on System Identification. Rotterdam, August
27. Norton J. Identification and application of bounded parameter models. Automatica 23 (1987) 497-507
28. Nummelin E. General irreducible Markov chains and nonnegative operators (1984), Cambridge University Press, Cambridge
29. Peterka V. Bayesian system identification. Automatica. A Journal of IFAC 17 (1981) 41-53
30. Robert C., and Casella G. Monte Carlo statistical methods (1999), Springer
31. Robert C.P. The Bayesian choice. 2 ed. (2001), Springer Verlag
32. Silverman B.W. Density estimation for statistics and data analysis. Monographs on statistics and applied probability (1986), Chapman & Hall, London
33. Spall J. Estimation via Markov Chain Monte-Carlo. IEEE Control Systems Magazine 23 (2003) 34-45
34. Tierney L. Markov chains for exploring posterior distributions. The American Statistician 22 (1994) 1701-1762 With discussion and a rejoinder by the author
35. Tjärnström F., and Ljung L. Estimating the variance in case of undermodeling using bootstrap. IEEE Transactions on Automatic Control AC-47 (2002) 395-398
36. Söderström T., and Stoica P. System identification (1989), Prentice Hall, New York
37. Walter E., and Piet-Lahanier H. Exact recursive polyhedral description of the feasible parameter set for bounded-error models. IEEE Transactions on Automatic Control AC-34 (1989) 911-914
38. Weyer E. Finite sample properties of system identification of ARX models under mixing conditions. Automatica. A Journal of IFAC 36 (2000) 1291-1299
39. Weyer E., Williamson R.C., and Mareels I.M.Y. Finite sample properties of linear model identification. IEEE Transactions on Automatic Control 44 (1999) 1370-1383