Twisted particle filters

Annals of Statistics

Volumn 42, Issue 1, 2014, Pages 115-141

  Whiteley, Nick ^a   Lee, Anthony ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Filtering; Sequential Monte Carlo

Indexed keywords

EID: 84988038832     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1167     Document Type: Article

References (30)

1. ANDRIEU, C., DOUCET, A. and HOLENSTEIN, R. (2010). Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. BStat. Methodol. 72 269-342. MR2758115
2. ANDRIEU, C. and ROBERTS, G. O. (2009). The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. 37 697-725. MR2502648
3. ANDRIEU, C. and VIHOLA, M. (2012). Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms. Available at arXiv:1210.1484v1 [math.PR].
4. ATHREYA, K. B. (2000). Change of measures for Markov chains and the L log L theorem for branching processes. Bernoulli 6 323-338. MR1748724
5. BUCKLEW, J. A., NEY, P. and SADOWSKY, J. S. (1990). Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains. J. Appl. Probab. 27 44-59. MR1039183
6. CÉROU, F., DEL MORAL, P. and GUYADER, A. (2011). A nonasymptotic theorem for unnormalized Feynman-Kac particle models. Ann. Inst. Henri Poincaré Probab. Stat. 47 629-649. MR2841068
7. CHOPIN, N. (2004). Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32 2385-2411. MR2153989
8. DEL MORAL, P. (2004). Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York. MR2044973
9. DEL MORAL, P. and GUIONNET, A. (1999). Central limit theorem for nonlinear filtering and interacting particle systems. Ann. Appl. Probab. 9 275-297. MR1687359
10. DEL MORAL, P. and GUIONNET, A. (2001). On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. Henri Poincaré Probab. Stat. 37 155-194. MR1819122
11. DEL MORAL, P. and JACOD, J. (2001). Interacting particle filtering with discrete time observations: Asymptotic behaviour in the Gaussian case. In Stochastics in Finite and Infinite Dimensions: In Honor of Gopinath Kallianpur (T. Hida, R. L. Karandikar, H. Kunita, B. S. Rajput, S. Watanabe and J. Xiong, eds.). Birkhäuser, Basel.
12. DOOB, J. L. (1994). Measure Theory. Graduate Texts in Mathematics 143. Springer, New York. MR1253752
13. DOUC, R. and MOULINES, E. (2008). Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann. Statist. 36 2344-2376. MR2458190
14. DOUC, R. and MOULINES, E. (2011). Asymptotic properties of the maximum likelihood estimation in misspecified Hidden Markov models. Available at arXiv:1110.0356.
15. DOUC, R., MOULINES, É. and OLSSON, J. (2009). Optimality of the auxiliary particle filter. Probab. Math. Statist. 29 1-28. MR2552996
16. DOUC, R., MOULINES, E. and OLSSON, J. (2012). Long-term stability of sequential Monte Carlo methods under verifiable conditions. Available at arXiv:1203.6898.
17. DOUCET, A., BRIERS, M. and SÉNÉCAL, S. (2006). Efficient block sampling strategies for sequential Monte Carlo methods. J. Comput. Graph. Statist. 15 693-711. MR2280152
18. FAVETTO, B. (2012). On the asymptotic variance in the central limit theorem for particle filters. ESAIM Probab. Stat. 16 151-164. MR2946125
19. GORDON, N. J., SALMOND, D. J. and SMITH, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar and Signal Processing, IEE Proceedings F 140 107-113.
20. JOHANSEN, A. M. and DOUCET, A. (2008). A note on auxiliary particle filters. Statist. Probab. Lett. 78 1498-1504. MR2528342
21. KIFER, Y. (1996). Perron-Frobenius theorem, large deviations, and random perturbations in random environments. Math. Z. 222 677-698. MR1406273
22. KÜNSCH, H. R. (2005). Recursive Monte Carlo filters: Algorithms and theoretical analysis. Ann. Statist. 33 1983-2021. MR2211077
23. LE GLAND, F. and OUDJANE, N. (2004). Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters. Ann. Appl. Probab. 14 144-187. MR2023019
24. LEGLAND, F. and OUDJANE, N. (2003). A robustification approach to stability and to uniform particle approximation of nonlinear filters: The example of pseudo-mixing signals. Stochastic Process. Appl. 106 279-316. MR1989630
25. LEROUX, B. G. (1992). Maximum-likelihood estimation for hidden Markov models. Stochastic Process. Appl. 40 127-143. MR1145463
26. OUDJANE, N. and RUBENTHALER, S. (2005). Stability and uniform particle approximation of nonlinear filters in case of non ergodic signals. Stoch. Anal. Appl. 23 421-448. MR2140972
27. PITT, M. K. and SHEPHARD, N. (1999). Filtering via simulation: Auxiliary particle filters. J. Amer. Statist. Assoc. 94 590-599. MR1702328
28. VAN HANDEL, R. (2009). Uniform time average consistency of Monte Carlo particle filters. Stochastic Process. Appl. 119 3835-3861. MR2552307
29. WHITELEY, N. (2013). Stability properties of some particle filters. Ann. Appl. Probab. 23 2500-2537. MR3127943
30. WHITELEY, N. and LEE, A. (2014). Supplement to "Twisted particle filters." DOI:10.1214/13-AOS1167SUPP.