Sequentially interacting Markov chain Monte Carlo methods

Annals of Statistics

Volumn 38, Issue 6, 2010, Pages 3387-3411

  Brockwell, Anthony ^a   Del Moral, Pierre ^b   Doucet, Arnaud ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b INRIA   (France)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Markov chain Monte Carlo; Normalizing constants; Sequential Monte Carlo; State space models

Indexed keywords

EID: 77949686856     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS747     Document Type: Article

References (28)

1. ANDRIEU, C., JASRA, A., DOUCET, A. and DEL MORAL, P. (2007). Nonlinear Markov chain Monte Carlo via self-interacting approximations. Technical report, Dept. Mathematics, Bristol Univ.
2. ANDRIEU, C. and MOULINES, E. (2006). On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16 1462-1505. MR2260070 (Pubitemid 44662199)
3. BERCU, B., DEL MORAL, P. and DOUCET, A. (2008). Fluctuations of interacting Markov chain Monte Carlo models. Technical Report Inria-00227536, INRIA Bordeaux Sud-Ouest. Available at http://hal.inria.fr/docs/00/23/92/48/PDF/ RR-6438.pdf.
4. BROCKWELL, A., ROJAS, A. and KASS, R. (2004). Recursive Bayesian decoding of motor cortical signals by particle filtering. J. Neurophysiology 91 1899-1907.
5. CARPENTER, J., CLIFFORD, P. and FEARNHEAD, P. (1999). An improved particle filter for non-linear problems. IEE Proceedings-Radar, Sonar and Navigation 146 2-7.
6. CHOPIN, N. (2002). A sequential particle filter method for static models. Biometrika 89 539-552. MR1929161
7. DEL MORAL, P. (2004). Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York. MR2044973
8. DEL MORAL, P. and DOUCET, A. (2010). Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations. Ann. Appl. Probab. 20 593-639. MR2650043
9. DEL MORAL, P., DOUCET, A. and JASRA, A. (2006). Sequential Monte Carlo samplers. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 411-436. MR2278333
10. DEL MORAL, P. and MICLO, L. (2004). On convergence of chains with occupational selfinteractions. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 325-346. MR2052266
11. DOUCET, A., GODSILL, S. J. and ANDRIEU, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statist. Comput. 10 197-208.
12. DOUCET, A., DE FREITAS, J. F. G. and GORDON, N. J., EDS. (2001). Sequential Monte Carlo Methods in Practice. Springer, New York. MR1847783
13. FOX, D. (2002). KLD-sampling: Adaptive particle filters. In Advances in Neural Information Processing Systems 14 713-720. MIT Press, Cambridge, MA.
14. GERLACH, R., CARTER, C. K. and KOHN, R. (1999). Diagnostics for time series analysis. J. Time Ser. Anal. 20 309-330. MR1693161
15. GILKS, W. R. and BERZUINI, C. (2001). Following a moving target - Monte Carlo inference for dynamic Bayesian models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 127-146. MR1811995
16. GLYNN, P. and MEYN, S. (1996). A Liapunov bound for solutions of Poisson's equation. Ann. Probab. 24 916-931. MR1404536
17. GREEN, P. J. (2003). Trans-dimensional Markov chain Monte carlo. In Highly Structured Stochastic Systems (P. J. Green, N. L. Hjort and S. Richardson, eds.) 179-196. Oxford Univ. Press, Oxford. MR2082410
18. KITAGAWA, G. (1996).Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J. Comput. Graph. Statist. 5 1-25. MR1380850
19. KOU, S., ZHOU, Q. and WONG, W. (2006). Equi-energy sampler with applications in statistical inference and statistical mechanics (with discussion). Ann. Statist. 34 1581-1652. MR2283711
20. JASRA, A., STEPHENS, D. A. and HOLMES, C. C. (2007). On population-based simulation for static inference. Statist. Comput. 17 263-279. MR2405807
21. LIU, J. S. (2001). Monte Carlo Strategies in Scientific Computing. Springer, New York. MR1842342
22. LIU, J. S. and CHEN, R. (1998). Sequential Monte Carlo for dynamic systems. J. Amer. Statist. Assoc. 93 1032-1044. MR1649198
23. LYMAN, E. and ZUCKERMAN, D. M. (2006). Resolution exchange simulation with incremental coarsening. J. Chem. Theory Comput. 2 656-666.
24. MENGERSEN, K. L. and TWEEDIE, R. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 101-121. MR1389882
25. PITT, M. K. and SHEPHARD, N. (1999). Filtering via simulation: Auxiliary particle filter. J. Amer. Statist. Assoc. 94 590-599. MR1702328
26. ROBERTS, G. O. and ROSENTHAL, J. S. (2007). Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms. J. Appl. Probab. 44 458-475. MR2340211
27. SEPTIER, F., PANG, S. K., CARMI, A. and GODSILL, S. J. (2009). On MCMC-based particle methods for Bayesian filtering: Application to multitarget tracking. In Proc. 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing 360-363. IEEE, Aruba.
28. SHIRYAEV, A. N. (1996). Probability, 2nd ed. Springer, New York. MR1368405