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Particle methods for maximum likelihood estimation in latent variable models
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Johansen, Adam M., Doucet, Arnaud and Davy, Manuel. (2008) Particle methods for maximum likelihood estimation in latent variable models. Statistics and Computing, Vol.18 (No.1). pp. 47-57. ISSN 0960-3174
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Official URL: http://dx.doi.org/10.1007/s11222-007-9037-8
Abstract
Standard methods for maximum likelihood parameter estimation in latent variable models rely on the Expectation-Maximization algorithm and its Monte Carlo variants. Our approach is different and motivated by similar considerations to simulated annealing; that is we build a sequence of artificial distributions whose support concentrates itself on the set of maximum likelihood estimates. We sample from these distributions using a sequential Monte Carlo approach. We demonstrate state of the art performance for several applications of the proposed approach.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Parameter estimation, Latent variables |
| Journal or Publication Title: | Statistics and Computing |
| Publisher: | Springer |
| ISSN: | 0960-3174 |
| Date: | 2008 |
| Volume: | Vol.18 |
| Number: | No.1 |
| Page Range: | pp. 47-57 |
| Identification Number: | 10.1007/s11222-007-9037-8 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Restricted or Subscription Access |
| References: | B. Amzal, F. Y. Bois, E. Parent, and C. P. Robert. Bayesian optimal design via interacting particle systems. Journal of the American Statistical Association, 101 (474):773–785, June 2006. N. Chopin. Central limit theorem for sequential Monte Carlo methods and its applications to Bayesian inference. Annals of Statistics, 32(6):2385–2411, December 2004. P. Del Moral. Feynman-Kac formulae: genealogical and interacting particle systems with applications. Probability and Its Applications. Springer Verlag, New York, 2004. P. Del Moral, A. Doucet, and A. Jasra. Sequential Monte Carlo samplers. Journal of the Royal Statistical Society B, 63(3):411–436, 2006. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM Algorithm. Journal of the Royal Statistical Society, Series B, 39:2–38, 1977. A. Doucet, N. de Freitas, and N. Gordon, editors. Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. Springer Verlag, New York, 2001. A. Doucet, S. J. Godsill, and C. P. Robert. Marginal maximum a posteriori estimation using Markov chain Monte Carlo. Statistics and Computing, 12:77–84, 2002. A. Doucet, M. Briers, and S. S´en´ecal. Efficient block sampling strategies for sequential Monte Carlo methods. Journal of Computational and Graphical Statistics, 15(3):693–711, 2006. M. D. Escobar and M. West. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90(430):577–588, June 1995. C. Gaetan and J.-F. Yao. A multiple-imputation Metropolis version of the EM algorithm. Biometrika, 90(3):643–654, 2003. C.-R. Hwang. Laplace’s method revisited: Weak convergence of probability measures. The Annals of Probability, 8(6):1177–1182, December 1980. E. Jacquier, M. Johannes, and N. Polson. MCMC maximum likelihood for latent state models. Journal of Econometrics, 137(2):615–640, April 2007. A. M. Johansen. Some Non-Standard Sequential Monte Carlo Methods With Ap- plications. Ph.D. thesis, University of Cambridge Department of Engineering, 2006. J. S. Liu and R. Chen. Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association, 93(443):1032–1044, September 1998. P. M¨uller, B. Sans´o, and M. de Iorio. Optimum Bayesian design by inhomogeneous Markov chain simulation. Journal of the American Statistical Association, 99: 788–798, 2004. C. P. Robert and G. Casella. Monte Carlo Statistical Methods. Springer Verlag, New York, second edition, 2004. C. P. Robert and D. M. Titterington. Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation. Sta- tistics and Computing, 8:145–158, 1998. K. Roeder. Density estimation with cofidence sets exemplified by superclusters and voids in galaxies. Journal of the American Statistical Association, 85(411): 617–624, September 1990. K. Roeder and L.Wasserman. Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92(439):894–902, September 1997. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/37383 |
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