Statistics and Computing

, Volume 27, Issue 6, pp 1677–1692 | Cite as

A second-order iterated smoothing algorithm

  • Dao Nguyen
  • Edward L. Ionides


Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method’s performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.


Iterated smoothing Sequential Monte Carlo State space model Hidden Markov model Parameter estimation 



This research was funded in part by National Science Foundation Grant DMS-1308919 and National Institutes of Health Grants 1-U54-GM111274 and 1-U01-GM110712.

Supplementary material

11222_2016_9711_MOESM_ESM.pdf (603 kb)
Supplementary material 1 (pdf 603 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of MichiganAnn ArborUSA

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