Simulated annealing for maximum A Posteriori parameter estimation of Hidden Markov models

IEEE Transactions on Information Theory

Volumn 46, Issue 3, 2000, Pages 994-1004

  Andrieu, Christophe ^a   Doucet, Arnaud ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; MARKOV PROCESSES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SIMULATED ANNEALING; STATE SPACE METHODS;

BAYESIAN ESTIMATION; DATA AUGMENTATION; EXPECTATION MAXIMIZATION ALGORITHM;

INFORMATION THEORY;

EID: 0034188341     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.841176     Document Type: Article

References (32)

1. L.R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE, vol. 77, pp. 257-286, 1989.
2. G.K. Kaleh and R. Vallet, "Joint parameter estimation and symbol detection for linear and nonlinear unknown channels," IEEE Trans. Commun., vol. 42, pp. 2046-2413, 1994.
3. R. Chen and T. Li, "Blind restoration of linearly degraded discrete signals by Gibbs sampling," IEEE Trans. Signal Processing, vol. 43, pp. 2410-2413, 1995.
4. O. Cappé, A. Doucet, M. Lavielle, and E. Moulines, "Simulation-based methods for blind maximum-likelihood filter identification," Signal Processing, vol. 73, no. 1, pp. 3-25, 1999.
5. S. Chib, "Calculating posterior distributions and modal estimates in Markov mixture models," J. Econometrics, vol. 75, pp. 79-97, 1996.
6. W. Quian and D. M. Titterington, "Estimation of parameters in hidden Markov models," Phil. Trans. Roy. Soc. London A, vol. 337, pp. 407-428, 1991.
7. C.P. Robert, G. Celeux, and J. Diebolt, "Bayesian estimation of hidden Markov models: A stochastic implementation," Statist. Probab. Lett., vol. 16, pp. 77-83, 1993.
8. C.P. Robert and D. M. Titterington, "Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum-likelihood estimation," Statist. Comp., vol. 8, pp. 145-158, 1998.
9. D.M. Titterington, A. F. M. Smith, and U. E. Makov, Statistical Analysis of Finite Mixture Distributions. New York: Wiley, 1985.
10. A.P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Statist. Soc. B., vol. 39, pp. 1-38, 1977.
11. G. Celeux and J. Diebolt, "The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem," Comp. Statist. Quat., vol. 2, pp. 73-82, 1985.
12. G.C. G. Wei and M. A. Tanner, "A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithm," J. Amer. Statist. Assoc., vol. 85, pp. 699-704, 1990.
13. J. Diebolt and E. H. S. Ip, "Stochastic EM: Method and application," in Markov Chain Monte Carlo in Practice, W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Eds. London, U.K.: Chapman & Hall, 1996.
14. J. Diebolt and C. P. Robert, "Estimation of finite mixture distributions through Bayesian sampling,"/ Roy. Statist. Soc. B, vol. 56, pp. 363-375, 1994
15. S. Chib and E. Greenberg, "Understanding the Metropolis-Hastings algorithm," Amer. Statistician, vol. 49, pp. 327-335, 1995.
16. L. Tierney, "Markov chains for exploring posterior distributions," Ann. Statist., vol. 22, pp. 1701-1762, 1994.
17. D. Mitra, F. Romeo, and A. Sangiovanni-Vincentelli, "Convergence and finite-time behavior of simulated annealing," Adv. Appl. Probab., vol. 18, pp. 747-771, 1986.
18. P.J. Van Laarhoven and E. H. L. Arts, Simulated Annealing: Theory and Applications. Amsterdam, The Netherlands: Reidel, 1987.
19. H. Haario and E. Sacksman, "Simulated annealing in general state space," Adv. Appl. Probab., vol. 23, pp. 866-893, 1991.
20. M.N. M. Van Lieshout, "Stochastic annealing for nearest-neighbor point processes with application to object recognition," Adv. Appl. Probab., vol. 26, pp. 281-300, 1994.
21. J.M. Bernardo and A. F. M. Smith, Bayesian Theory. New York: Wiley, 1995.
22. C.K. Carter and R. Kohn, "On Gibbs sampling for state space models," Biometrika, vol. 81, pp. 541-553, 1994.
23. L. Devroye, Non-Uniform Random Variate Generation. New York: Springer, 1986.
24. S.P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability. New York: Springer-Verlag, 1993.
25. C. Hwang, "Laplace's method revisited: Weak convergence of probability measures," A. Probab., vol. 8, pp. 1177-1182, 1980.
26. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images, " lEEETrans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, 1984.
27. B.G. Leroux and M. L. Puterman, "Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models," Biometrics, vol. 48, pp. 545-558, 1992.
28. U. Hoist, G. Lindgren, J. Hoist, and M. Thuvesholment, "Recursive estimation in switching autoregressions with a Markov regime," J. Time Ser. Anal, vol. 15, pp. 489-506, 1994.
29. A.B. Poritz, "Linear predictive hidden Markov models and the speech signal," in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Paris, France, 1982, pp. 1291-1294.
30. S. Chib, "Bayesian estimation of regressions with autoregressive errors: A Gibbs sampling approach," J. Econometrics, vol. 58, pp. 275-294, 1993.
31. B.D. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
32. P.A. Devijver, "Baum's forward-backward algorithm revisited," Pattern Recogn. Lett., vol. 3, pp. 369-373, 1985.