Convergence Properties of Weighted Particle Islands with Application to the Double Bootstrap Algorithm

References

• B. Balasingam, M. Bolić, P. M. Djurić, and J. Míguez. Efficient distributed resampling for particle filters. In 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 3772–3775, May 2011.Google Scholar
• M. Bolić, P. M. Djurić, and Sangjin Hong. Resampling algorithms and architectures for distributed particle filters. IEEE Transactions on Signal Processing, 53(7):2442–2450, July 2005.Google Scholar
• O. Cappé and E. Moulines. On the use of particle filtering for maximum likelihood parameter estimation. In European Signal Processing Conference (EUSIPCO), Antalya, Turkey, September 2005.Google Scholar
• O. Cappé, E. Moulines, and T. Rydén. Inference in Hidden Markov Models. Springer, 2005. MR2159833Google Scholar
• F. Cérou, P. Del Moral, T. Furon, and A. Guyader. Sequential Monte Carlo for rare event estimation. Stat. Comput., 22(3):795–808, 2012.Google Scholar
• N. Chopin. A sequential particle filter method for static models. Biometrika, 89:539–552, 2002.Google Scholar
• N. Chopin. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist., 32(6):2385–2411, 2004. MR2153989Google Scholar
• N. Chopin, P. Jacob, and O. Papaspiliopoulos. SMC2: A sequential Monte Carlo algorithm with particle Markov chain Monte Carlo updates. J. Roy. Statist. Soc. B, 75(3):397–426, 2013.Google Scholar
• D. Crisan and B. L. Rozovskii, editors. The Oxford handbook of nonlinear filtering. Oxford–New York, Oxford University Press, 2011.Google Scholar
• P. Del Moral. Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. Springer, 2004. MR2044973Google Scholar
• P. Del Moral and J. Garnier. Genealogical particle analysis of rare events. Ann. Appl. Probab., 15(4):2496–2534, 2005. MR2187302Google Scholar
• P. Del Moral and A. Guionnet. Central limit theorem for nonlinear filtering and interacting particle systems. Ann. Appl. Probab., 9(2):275–297, 1999.Google Scholar
• P. Del Moral and A. Guionnet. On the stability of interacting processes with applications to filtering and genetic algorithms. Annales de l’Institut Henri Poincaré, 37:155–194, 2001.Google Scholar
• R. Douc, A. Garivier, E. Moulines, and J. Olsson. Sequential Monte Carlo smoothing for general state space hidden Markov models. Ann. Appl. Probab., 21(6):2109–2145, 2011. MR2895411Google Scholar
• R. Douc and E. Moulines. Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann. Statist., 36(5):2344–2376, 2008.Google Scholar
• R. Douc, É. Moulines, and J. Olsson. Optimality of the auxiliary particle filter. Probab. Math. Statist., 29(1):1–28, 2009.Google Scholar
• R. Douc, E. Moulines, and J. Olsson. Long-term stability of sequential Monte Carlo methods under verifiable conditions. Ann. Appl. Probab., 24(5):1767–1802, 2014. MR3226163Google Scholar
• R. Douc, E. Moulines, and D. Stoffer. Nonlinear Time Series: Theory, Methods and Applications with R Examples. Chapman & Hall/CRC Texts in Statistical Science, 2014.Google Scholar
• A. Doucet, N. De Freitas, and N. Gordon, editors. Sequential Monte Carlo Methods in Practice. Springer, New York, 2001.Google Scholar
• K. Heine and N. Whiteley. Fluctuations, stability and instability of a distributed particle filter with local exchange. ArXiv e-prints, May 2015.Google Scholar
• A. Kong, J. S. Liu, and W. Wong. Sequential imputation and Bayesian missing data problems. J. Am. Statist. Assoc., 89(278–288):590–599, 1994.Google Scholar
• H. R. Künsch. Recursive Monte-Carlo filters: Algorithms and theoretical analysis. Ann. Statist., 33(5):1983–2021, 2005. MR2211077Google Scholar
• J. S. Liu. Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Stat. Comput., 6:113–119, 1996.Google Scholar
• J.S. Liu. Monte Carlo Strategies in Scientific Computing. Springer, New York, 2001.Google Scholar
• J. Olsson, O. Cappé, R. Douc, and E. Moulines. Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models. Bernoulli, 14(1):155–179, 2008. arXiv:math.ST/0609514.Google Scholar
• M. K. Pitt and N. Shephard. Filtering via simulation: Auxiliary particle filters. J. Am. Statist. Assoc., 94(446):590–599, 1999.Google Scholar
• B. Ristic, M. Arulampalam, and A. Gordon. Beyond Kalman Filters: Particle Filters for Target Tracking. Artech House, 2004.Google Scholar
• O. Rosen and A. Medvedev. Efficient parallel implementation of state estimation algorithms on multicore platforms. IEEE Transactions on Control Systems Technology, 21(1):107–120, Jan 2013.Google Scholar
• A. C. Sankaranarayanan, A. Srivastava, and R. Chellappa. Algorithmic and architectural optimizations for computationally efficient particle filtering. IEEE Transactions on Image Processing, 17(5):737–748, May 2008. MR2516598Google Scholar
• S. Sutharsan, T. Kirubarajan, T. Lang, and M. Mcdonald. An optimization-based parallel particle filter for multitarget tracking. IEEE Transactions on Aerospace and Electronic Systems, 48(2):1601–1618, April 2012.Google Scholar
• C. Vergé, C. Dubarry, P. Del Moral, and E. Moulines. On parallel implementation of sequential Monte Carlo methods: the island particle model. Statistics and Computing, 23, 2013.Google Scholar