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Likelihood computation for hidden Markov models via generalized two-filter smoothing

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  • Persing, Adam
  • Jasra, Ajay

Abstract

We introduce an estimate for the likelihood of hidden Markov models (HMMs) using sequential Monte Carlo (SMC) approximations of the generalized two-filter smoothing decomposition (Briers et al., 2010). This estimate is unbiased and a central limit theorem (CLT) is established. The new estimate is also investigated from a numerical perspective.

Suggested Citation

  • Persing, Adam & Jasra, Ajay, 2013. "Likelihood computation for hidden Markov models via generalized two-filter smoothing," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1433-1442.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:5:p:1433-1442
    DOI: 10.1016/j.spl.2013.02.005
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    References listed on IDEAS

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    1. Mark Briers & Arnaud Doucet & Simon Maskell, 2010. "Smoothing algorithms for state–space models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 61-89, February.
    2. Whiteley, Nick & Kantas, Nikolas & Jasra, Ajay, 2012. "Linear variance bounds for particle approximations of time-homogeneous Feynman–Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1840-1865.
    3. Paul Fearnhead & David Wyncoll & Jonathan Tawn, 2010. "A sequential smoothing algorithm with linear computational cost," Biometrika, Biometrika Trust, vol. 97(2), pages 447-464.
    4. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
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