Estimation via Markov Chian Monte Carlo

IEEE Control Systems

Volumn 23, Issue 2, 2003, Pages 34-45

  Spall, James C ^a  

^a JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; SAMPLING;

GIBBS SAMPLING; MARKOV CHAIN MONTE CARLO; METROPOLIS-HASTINGS SAMPLING;

STATE ESTIMATION;

EID: 0037389378     PISSN: 1066033X     EISSN: None     Source Type: Journal    
DOI: 10.1109/MCS.2003.1188770     Document Type: Article

References (35)

1. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys., vol. 21, pp. 1087-1092, 1953.
2. W.K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, vol. 57, pp. 97-109, 1970.
3. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, 1984.
4. M. Tanner and W. Wong, “The calculation of posterior distributions by data augmentation (with discussion),” J. Amer. Statist. Assoc., vol. 82, pp. 528-550, 1987.
5. A.E. Gelfand and A.F.M. Smith, “Sampling-based approaches to calculating marginal densities,” J. Amer. Statist. Assoc., vol. 85, pp. 399-409, 1990.
6. J. Besag, P. Green, D. Higdon, and K. Mengersen, “Bayesian computation and stochastic systems,” Statist. Sci., vol. 10, pp. 3-66, 1995.
7. O. Cappé and C.P. Robert, “Markov chain Monte Carlo: 10 years and still running!,” J. Amer. Statist. Assoc., vol. 95, pp. 1282-1286, 2000.
8. A.E.Gelfand, “Gibbssampling,” J. Amer. Statist. Assoc., vol.95, pp. 1300-1304, 2000.
9. M. Evans and T. Swartz, “Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems,” Statist. Sci., vol. 10, pp. 254-272, 1995.
10. W.R. Gilks, S. Richardson, and D.J. Spiegelhalter, Eds., Markov Chain Monte Carlo in Practice. London: Chapman and Hall, 1996.
11. C.P. Robert and G. Casella, Monte Carlo Statistical Methods. New York: Springer-Verlag, 1999.
12. M.-H. Chen, Q.-M. Shao, and J.G. Ibrahim, Monte Carlo Methods in Bayesian Computation. New York: Springer-Verlag, 2000.
13. J.S. Liu, Monte Carlo Strategies in Scientific Computing. NewYork: Springer, 2001.
14. A. Doucet, A. Logothetis, and V. Krishnamurthy, “Stochastic sampling algorithms for state estimation in jump Markov linear systems,” IEEE Trans. Automat. Contr., vol. 45, no. 2, pp. 188-202, 2000.
15. R.Y. Rubinstein and B. Melamed, Modern Simulation and Modeling. New York: Wiley, 1998.
16. E. Parzen,Stochastic Processes. New York: Holden-Day, 1962.
17. S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671-680, 1983.
18. C. Andrieu, L. Breyer, and A. Doucet, “Convergence of simulated annealing using Foster-Lyapunov criteria,” J. Appl. Prob., vol. 38, no. 4, pp. 975-994, 2001.
19. J.C. Spall, Introduction to Stochastic Search and Optimization. Hoboken, NJ: Wiley, 2003.
20. S. Chib and E. Greenberg, “Understanding the Metropolis-Hastings algorithm,” Amer. Statist., vol. 49, pp. 327-335, 1995.
21. W.R. Gilks, G.O. Roberts, and S.K. Sahu, “Adaptive Markov chain Monte Carlo through regeneration,” J. Amer. Statist. Assoc., vol. 93, pp. 1045-1054, 1998.
22. G.O. Roberts and J.S. Rosenthal, “Optimal scaling for various Metropolis-Hastings algorithms,” Statist. Sci., vol. 16, no. 4, pp. 351-367, 2001.
23. G. Casella and E.I. George, “Explaining the Gibbs sampler,” Amer. Statist., vol. 46, pp. 167-174, 1992.
24. K.V. Mardia, J.T. Kent, and J.M. Bibby, Multivariate Analysis. New York: Academic, 1979.
25. P.J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika, vol. 82, no. 4, pp. 711-732, 1995.
26. S. Chib, “Marginal likelihood from the Gibbs sampler,” J. Amer. Statist. Assoc., vol. 90, pp. 1313-1321, 1995.
27. J.E. Handschin and D.Q. Mayne, “Monte Carlo techniques to estimate the conditional expectation in multistage, nonlinear filtering,” Int. J. Contr., vol. 9, pp. 547-559, 1969.
28. B.P. Carlin, N.G. Polson, and D.S. Stoffer, “A Monte Carlo approach to nonnormal and nonlinear state-space modeling,” J. Amer. Statist. Assoc., vol. 87, pp. 493-500, 1992.
29. N.J. Gordon, D.J. Salmond, and A.F.M. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” Proc. Inst. Elec. Eng., vol. 140, pt. F, 1993, pp. 107-113.
30. C.K. Carter and R. Kohn, “On Gibbs sampling for state-space models,” Biometrika, vol. 81, pp. 541-553, 1994.
31. J. Geweke and H. Tanizaki, “Bayesian estimation of state-space models using the Metropolis-Hastings algorithm within Gibbs sampling,” Comput. Statisti. Data Anal., vol. 37, pp. 151-170, 2001.
32. J.C. Spall, “The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions,” Automatica, vol. 31, pp. 1513-1517, 1995.
33. J.L. Maryak, J.C. Spall, and B.D. Heydon, “Use of the Kalman filter for inference in state-space models with unknown noise distributions,” in Proc. American Control Conf., Albuquerque, NM, 1997, pp. 2127-2132.
34. J.C. Spall and S.D. Hill, “Least-informative Bayesian prior distributions for finite samples based on information theory,” IEEE Trans. Automatic Contr., vol. 35, pp. 580-583, 1990.
35. D.L. Alspach and H.W. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations,” IEEE Trans. Automat. Contr., vol. AC-17, pp. 439-448, 1972.