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On the use of sequential Monte Carlo methods for approximating smoothing functionals, with application to fixed parameter estimation

Olsson, Jimmy LU ; Cappé, Olivier; Douc, Randal and Moulines, Éric (2007) Conference Oxford sur les méthodes de Monte Carlo séquentielles, 2006 In ESAIM Proceedings 19. p.6-11
Abstract
Sequential Monte Carlo (SMC) methods have demonstrated a strong potential for inference on the state variables in Bayesian dynamic models. In this context, it is also often needed to calibrate model parameters. To do so, we consider block maximum likelihood estimation based either on EM (Expectation-Maximization) or gradient methods. In this approach, the key ingredient is the computation of smoothed sum functionals of the hidden states, for a given value of the model parameters. It has been observed by several authors that using standard SMC methods for this smoothing task requires a substantial number of particles and may be unreliable for larger observation sample sizes. We introduce a simple variant of the basic sequential smoothing... (More)
Sequential Monte Carlo (SMC) methods have demonstrated a strong potential for inference on the state variables in Bayesian dynamic models. In this context, it is also often needed to calibrate model parameters. To do so, we consider block maximum likelihood estimation based either on EM (Expectation-Maximization) or gradient methods. In this approach, the key ingredient is the computation of smoothed sum functionals of the hidden states, for a given value of the model parameters. It has been observed by several authors that using standard SMC methods for this smoothing task requires a substantial number of particles and may be unreliable for larger observation sample sizes. We introduce a simple variant of the basic sequential smoothing approach based on forgetting ideas. This modification, which is transparent in terms of computation time, reduces the variability of the approximation of the sum functional. Under suitable regularity assumptions, it is shown that this modification indeed allows a tighter control of the Lp error of the approximation. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Sequential Monte Carlo, Parameter Estimation, Filtering and Smoothing
in
ESAIM Proceedings
volume
19
pages
6 pages
conference name
Conference Oxford sur les méthodes de Monte Carlo séquentielles, 2006
ISSN
1270-900X
DOI
10.1051/proc:071902
language
English
LU publication?
yes
id
d8f86f42-995c-4be5-a481-b2f13938ba0d (old id 1271976)
date added to LUP
2009-06-03 17:19:38
date last changed
2016-04-16 06:12:31
@misc{d8f86f42-995c-4be5-a481-b2f13938ba0d,
  abstract     = {Sequential Monte Carlo (SMC) methods have demonstrated a strong potential for inference on the state variables in Bayesian dynamic models. In this context, it is also often needed to calibrate model parameters. To do so, we consider block maximum likelihood estimation based either on EM (Expectation-Maximization) or gradient methods. In this approach, the key ingredient is the computation of smoothed sum functionals of the hidden states, for a given value of the model parameters. It has been observed by several authors that using standard SMC methods for this smoothing task requires a substantial number of particles and may be unreliable for larger observation sample sizes. We introduce a simple variant of the basic sequential smoothing approach based on forgetting ideas. This modification, which is transparent in terms of computation time, reduces the variability of the approximation of the sum functional. Under suitable regularity assumptions, it is shown that this modification indeed allows a tighter control of the Lp error of the approximation.},
  author       = {Olsson, Jimmy and Cappé, Olivier and Douc, Randal and Moulines, Éric},
  issn         = {1270-900X},
  keyword      = {Sequential Monte Carlo,Parameter Estimation,Filtering and Smoothing},
  language     = {eng},
  pages        = {6--11},
  series       = {ESAIM Proceedings},
  title        = {On the use of sequential Monte Carlo methods for approximating smoothing functionals, with application to fixed parameter estimation},
  url          = {http://dx.doi.org/10.1051/proc:071902},
  volume       = {19},
  year         = {2007},
}