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

Free access article

Issue		ESAIM: PROC Volume 19, 2007 Conference Oxford sur les méthodes de Monte Carlo séquentielles


Page(s)		6 - 11
DOI		10.1051/proc:071902
Published online		30 October 2007

ESAIM: Proc., 2007, Vol. 19, pp. 6-11
DOI: 10.1051/proc:071902

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

Jimmy Olsson¹, Olivier Cappé², Randal Douc³ and Éric Moulines²

¹ Center for Mathematical Sciences, Lund University, Sweden
² Laboratoire Traitement et Communication de l'Information, CNRS / GET Télécom Paris, France
³ Centre de Mathématiques APpliquées, Ecole Polytechnique, France

(Published online: 30 October 2007)

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 L_p error of the approximation.

Mathematics Subject Classification. 62M20, 93E25

Key words: Sequential Monte Carlo, Filtering and Smoothing, Parameter Estimation

© EDP Sciences, ESAIM 2007

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.