SMC2: An efficient algorithm for sequential analysis of state space models

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 75, Issue 3, 2013, Pages 397-426

  Chopin, N ^a   Jacob, P E ^b   Papaspiliopoulos, O ^c  

^a CREST   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Iterated batch importance sampling; Particle filtering; Particle Markov chain Monte Carlo methods; Sequential Monte Carlo sampling; State space models

Indexed keywords

EID: 84878260706     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2012.01046.x     Document Type: Article

References (51)

1. Andrieu, C., Doucet, A. and Holenstein, R. (2010) Particle Markov chain Monte Carlo methods (with discussion). J. R. Statist. Soc. B, 72, 269-342.
2. Andrieu, C. and Roberts, G. (2009) The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist., 37, 697-725.
3. Barndorff-Nielsen, O. E. and Shephard, N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Statist. Soc. B, 63, 167-241.
4. Barndorff-Nielsen, O. E. and Shephard N. (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J. R. Statist. Soc. B, 64, 253-280.
5. Black, F. (1976) Studies of stock price volatility changes. Proc. Econ. Statist. Sect. Am. Statist. Ass., 81, 177-181.
6. Cappé, O., Guillin, A., Marin, J. M. and Robert, C. (2004) Population Monte Carlo. J. Computnl Graph. Statist., 23, 907-929.
7. Cappé, O., Moulines, E. and Rydén, T. (2005) Inference in Hidden Markov Models. New York: Springer.
8. Carpenter, J., Clifford, P. and Fearnhead, P. (1999) Improved particle filter for nonlinear problems. IEE Proc. Rad. Son. Navign, 146, 2-7.
9. Carvalho, C., Johannes, M., Lopes, H. and Polson, N. (2010) Particle learning and smoothing. Statist. Sci., 25, 88-106.
10. Cérou, F., Del Moral, P. and Guyader, A. (2011) A nonasymptotic theorem for unnormalized Feynman-Kac particle models. Ann. Inst. H. Poin., 47, 629-649.
11. Chernov, M., Ronald Gallant, A., Ghysels, E. and Tauchen, G. (2003) Alternative models for stock price dynamics. J. Econmetr., 116, 225-257.
12. Chopin, N. (2002) A sequential particle filter for static models. Biometrika, 89, 539-552.
13. Chopin, N. (2004) Central Limit Theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist., 32, 2385-2411.
14. Chopin, N. (2007) Inference and model choice for sequentially ordered hidden Markov models. J. R. Statist. Soc. B, 69, 269-284.
15. Crisan, D. and Doucet, A. (2002) A survey of convergence results on particle filtering methods for practitioners. IEEE Trans. Sig. Process., 50, 736-746.
16. Del Moral, P. (2004) Feynman-Kac Formulae. New York: Springer.
17. Del Moral, P., Doucet, A. and Jasra, A. (2006) Sequential Monte Carlo samplers. J. R. Statist. Soc. B, 68, 411-436.
18. Del Moral, P. and Guionnet, A. (1999) Central limit theorem for nonlinear filtering and interacting particle systems. Ann. Appl. Probab., 9, 275-297.
19. Douc, R. and Moulines, E. (2008) Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann. Statist., 36, 2344-2376.
20. Doucet, A., de Freitas, N. and Gordon, N. J. (2001) Sequential Monte Carlo Methods in Practice. New York: Springer.
21. Doucet, A., Godsill, S. and Andrieu, C. (2000) On Sequential Monte Carlo sampling methods for Bayesian filtering. Statist. Comput., 10, 197-208.
22. Doucet, A., Kantas, N., Singh, S. and Maciejowski, J. (2009) An overview of Sequential Monte Carlo methods for parameter estimation in general state-space models. In Proc. International Federation of Automatic Control Meet. System Identification.
23. Doucet, A., Poyiadjis, G. and Singh, S. (2011) Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation. Biometrika, 98, 65-80.
24. Fearnhead, P. (2002) MCMC, sufficient statistics and particle filters. Statist. Comput., 11, 848-862.
25. Fearnhead, P., Papaspiliopoulos, O. and Roberts, G. O. (2008) Particle filters for partially observed diffusions. J. R. Statist. Soc. B, 70, 755-777.
26. Fearnhead, P., Papaspiliopoulos, O., Roberts, G. O. and Stuart, A. (2010a) Random-weight particle filtering of continuous time processes. J. R. Statist. Soc. B, 72, 497-512.
27. Fearnhead, P., Wyncoll, D. and Tawn, J. (2010b) A sequential smoothing algorithm with linear computational cost. Biometrika, 97, 447-464.
28. Fulop, A. and Duan, J. (2011) Marginalized sequential monte carlo samplers. Technical Report SSRN1837772.
29. Fulop, A. and Li, J. (2011) Robust and efficient learning: a marginalized resample-move approach. Technical Report SSRN1724203.
30. Gaetan, C. and Grigoletto, M. (2004) Smoothing sample extremes with dynamic models. Extremes, 7, 221-236.
31. Gilks, W. R. and Berzuini, C. (2001) Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. R. Statist. Soc. B, 63, 127-146.
32. Gordon, N. J., Salmond, D. J. and Smith, A. F. M. (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc. F, 140, 107-113.
33. Griffin, J. and Steel, M. (2006) Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility. J. Econmetr., 134, 605-644.
34. Harvey, A. and Shephard, N. (1996) Estimation of an asymmetric stochastic volatility model for asset returns. J. Bus. Econ. Statist., 14, 429-434.
35. Jasra, A., Stephens, D. and Holmes, C. (2007) On population-based simulation for static inference. Statist. Comput., 17, 263-279.
36. Kim, S., Shephard, N. and Chib, S. (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Rev. Econ. Stud., 65, 361-393.
37. Kitagawa, G. (1998) A self-organizing state-space model. J. Am. Statist. Ass., 93, 1203-1215.
38. Koop, G. and Potter, S. M. (2007) Forecasting and estimating multiple change-point models with an unknown number of change-points. Rev. Econ. Stud., 74, 763-789.
39. Künsch, H. (2001) State space and hidden Markov models. In Complex Stochastic Systems (eds O. E. Barndorff-Nielsen, D. R. Cox and C. Klüppelberg ), pp. 109-173. Boca Raton: Chapman and Hall.
40. Liu, J. S. (2008) Monte Carlo Strategies in Scientific Computing. New York: Springer.
41. Liu, J. and Chen, R. (1998) Sequential Monte Carlo methods for dynamic systems. J. Am. Statist. Ass., 93, 1032-1044.
42. Liu, J. and West, M. (2001) Combined parameter and state estimation in simulation-based filtering. In Sequential Monte Carlo Methods in Practice (eds A. Doucet, N. de Freitas and N. J. Gordon ), pp. 197-223. New York: Springer
43. Neal, R. M. (2001) Annealed importance sampling. Statist. Comput., 11, 125-139.
44. Oudjane, N. and Rubenthaler, S. (2005) Stability and uniform particle approximation of nonlinear filters in case of non ergodic signals. Stoch. Anal. Applic., 23, 421-448.
45. Papaspiliopoulos, O., Roberts, G. O. and Sköld, M. (2007) A general framework for the parametrization of hierarchical models. Statist. Sci., 22, 59-73.
46. Peters, G., Hosack, G. and Hayes, K. (2010) Ecological non-linear state space model selection via adaptive particle markov chain monte carlo. Arxiv Preprint arXiv:1005.2238.
47. Roberts, G. O., Papaspiliopoulos, O. and Dellaportas, P. (2004) Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. J. R. Statist. Soc. B, 66, 369-393.
48. Robinson, M. E. and Tawn, J. A. (1995) Statistics for exceptional athletics records. Appl. Statist., 44, 499-511.
49. Silva, R., Giordani, P., Kohn, R. and Pitt, M. (2009) Particle filtering within adaptive Metropolis Hastings sampling. Arxiv Preprint arXiv:0911.0230.
50. Storvik, G. (2002) Particle filters for state-space models with the presence of unknown static parameters. IEEE Trans. Sig. Process., 50, 281-289.
51. Whiteley, N. (2011) Stability properties of some particle filters. Arxiv Preprint arXiv:1109.6779.