Stability properties of some particle filters

Annals of Applied Probability

Volumn 23, Issue 6, 2013, Pages 2500-2537

  Whiteley, Nick ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Hidden markov model; Particle filter; Sequential monte carlo

Indexed keywords

EID: 84888340792     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AAP909     Document Type: Article

References (25)

1. 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.
2. CHOPIN, N. (2004). Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32 2385-2411. MR2153989. (Pubitemid 40936677)
3. DEL MORAL, P. (2004). Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York. MR2044973.
4. DEL MORAL, P., DOUCET, A. and SINGH, S. S. (2010). A backward particle interpretation of Feynman-Kac formulae. M2AN Math. Model. Numer. Anal. 44 947-975. MR2731399.
5. DEL MORAL, P., DOUCET, A. and JASRA, A. (2012). On adaptive resampling strategies for sequential Monte Carlo methods. Bernoulli 18 252-278. MR2888706.
6. 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.
7. 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.
8. DEL MORAL, P., PATRAS, F. and RUBENTHALER, S. (2009). Tree based functional expansions for Feynman-Kac particle models. Ann. Appl. Probab. 19 778-825. MR2521888.
9. DOUC, R. and MOULINES, E. (2008). Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann. Statist. 36 2344-2376. MR2458190.
10. DOUC, R., FORT, G., MOULINES, E. and PRIOURET, P. (2009). Forgetting the initial distribution for hidden Markov models. Stochastic Process. Appl. 119 1235-1256. MR2508572.
11. DOUC, R., GARIVIER, A., MOULINES, E. and OLSSON, J. (2011). Sequential Monte Carlo smoothing for general state space hidden Markov models. Ann. Appl. Probab. 21 2109-2145. MR2895411.
12. DOUCET, A., GODSILL, S. and ANDRIEU, C. (2000). On sequentialMonte Carlo sampling methods for Bayesian filtering. Stat. Comput. 10 197-208.
13. FAVETTO, B. (2012). On the asymptotic variance in the central limit theorem for particle filters. ESAIM Probab. Stat. 16 151-164. MR2946125.
14. GORDON, N. J., SALMOND, D. J. and SMITH, A. F. M. (1993). Novel approach to nonlinear/non- Gaussian Bayesian state estimation. In IEE Proceedings F on Radar and Signal Processing 140 107-113. IET.
15. HEINE, K. and CRISAN, D. (2008). Uniform approximations of discrete-time filters. Adv. in Appl. Probab. 40 979-1001. MR2488529.
16. KLEPTSYNA, M. L. and VERETENNIKOV, A. Y. (2008). On discrete time ergodic filters with wrong initial data. Probab. Theory Related Fields 141 411-444. MR2391160.
17. KONTOYIANNIS, I. and MEYN, S. P. (2005). Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes. Electron. J. Probab. 10 61-123 (electronic). MR2120240. (Pubitemid 40447601)
18. KÜNSCH, H. R. (2005). Recursive Monte Carlo filters: Algorithms and theoretical analysis. Ann. Statist. 33 1983-2021. MR2211077. (Pubitemid 43059668)
19. 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. (Pubitemid 36742401)
20. LEGLAND, 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. (Pubitemid 41449255)
21. 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. (Pubitemid 40801686)
22. PITT, M. K. and SHEPHARD, N. (1999). Filtering via simulation: Auxiliary particle filters. J. Amer. Statist. Assoc. 94 590-599. MR1702328.
23. VAN HANDEL, R. (2009). Uniform time average consistency ofMonte Carlo particle filters. Stochastic Process. Appl. 119 3835-3861. MR2552307.
24. WHITELEY, N. (2012). Sequential Monte Carlo samplers: Error bounds and insensitivity to initial conditions. Stoch. Anal. Appl. 30 774-798. MR2966098.
25. WHITELEY, N., KANTAS, N. and JASRA, A. (2012). Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae. Stochastic Process. Appl. 122 1840-1865. MR2914774.