On the two-filter approximations of marginal smoothing distributions in general state space models

Thi Ngoc Minh Nguyen (1) , Sylvain Le Corff (2) , Éric Moulines (3, 4)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 XPOP - Modélisation en pharmacologie de population

A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state given future observations.

Mots clés: Smoothing distributions; Hidden Markov Models; Sequential Monte Carlo methods; Two-filter algorithms

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Thi Ngoc Minh Nguyen, Sylvain Le Corff, Éric Moulines. On the two-filter approximations of marginal smoothing distributions in general state space models. Advances in Applied Probability, 2018, 50 (1), pp.154-177. ⟨10.1017/apr.2018.8⟩. ⟨hal-01319747⟩