IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v19y2017i3d10.1007_s11009-016-9511-x.html
   My bibliography  Save this article

Biased Online Parameter Inference for State-Space Models

Author

Listed:
  • Pierre Del Moral

    (Universite de Bordeaux I)

  • Ajay Jasra

    (National University of Singapore)

  • Yan Zhou

    (National University of Singapore)

Abstract

We consider Bayesian online static parameter estimation for state-space models. This is a very important problem, but is very computationally challenging as the state-of-the art methods that are exact, often have a computational cost that grows with the time parameter; perhaps the most successful algorithm is that of SM C2 (Chopin et al., J R Stat Soc B 75: 397–426 2013). We present a version of the SM C2 algorithm which has computational cost that does not grow with the time parameter. In addition, under assumptions, the algorithm is shown to provide consistent estimates of expectations w.r.t. the posterior. However, the cost to achieve this consistency can be exponential in the dimension of the parameter space; if this exponential cost is avoided, typically the algorithm is biased. The bias is investigated from a theoretical perspective and, under assumptions, we find that the bias does not accumulate as the time parameter grows. The algorithm is implemented on several Bayesian statistical models.

Suggested Citation

  • Pierre Del Moral & Ajay Jasra & Yan Zhou, 2017. "Biased Online Parameter Inference for State-Space Models," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 727-749, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9511-x
    DOI: 10.1007/s11009-016-9511-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9511-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-016-9511-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. 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.
    3. Centanni, Silvia & Minozzo, Marco, 2006. "A Monte Carlo Approach to Filtering for a Class of Marked Doubly Stochastic Poisson Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1582-1597, December.
    4. Nicholas G. Polson & Jonathan R. Stroud & Peter Müller, 2008. "Practical filtering with sequential parameter learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 413-428, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Naoki Awaya & Yasuhiro Omori, 2019. "Particle rolling MCMC," CIRJE F-Series CIRJE-F-1110, CIRJE, Faculty of Economics, University of Tokyo.
    2. Axel Finke & Adam Johansen & Dario Spanò, 2014. "Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 577-609, June.
    3. Naoki Awaya & Yasuhiro Omori, 2017. "Particle rolling MCMC with Double Block Sampling: Conditional SMC Update Approach," CIRJE F-Series CIRJE-F-1066, CIRJE, Faculty of Economics, University of Tokyo.
    4. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    5. James Martin & Ajay Jasra & Emma McCoy, 2013. "Inference for a class of partially observed point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 413-437, June.
    6. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).
    7. Jin, Guang & Matthews, David E. & Zhou, Zhongbao, 2013. "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 7-20.
    8. Naoki Awaya & Yasuhiro Omori, 2021. "Particle Rolling MCMC with Double-Block Sampling ," CIRJE F-Series CIRJE-F-1175, CIRJE, Faculty of Economics, University of Tokyo.
    9. Calvet, Laurent-Emmanuel & Czellar , Veronika, 2011. "state-observation sampling and the econometrics of learning models," HEC Research Papers Series 947, HEC Paris.
    10. Nicolas Chopin & Mathieu Gerber, 2017. "Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes," Working Papers 2017-35, Center for Research in Economics and Statistics.
    11. Turnbull, Kathryn & Nemeth, Christopher & Nunes, Matthew & McCormick, Tyler, 2023. "Sequential estimation of temporally evolving latent space network models," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    12. Fulop, Andras & Heng, Jeremy & Li, Junye & Liu, Hening, 2022. "Bayesian estimation of long-run risk models using sequential Monte Carlo," Journal of Econometrics, Elsevier, vol. 228(1), pages 62-84.
    13. Owen Jamie & Wilkinson Darren J. & Gillespie Colin S., 2015. "Likelihood free inference for Markov processes: a comparison," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(2), pages 189-209, April.
    14. Herbst, Edward & Schorfheide, Frank, 2019. "Tempered particle filtering," Journal of Econometrics, Elsevier, vol. 210(1), pages 26-44.
    15. Cozzini, Alberto & Jasra, Ajay & Montana, Giovanni & Persing, Adam, 2014. "A Bayesian mixture of lasso regressions with t-errors," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 84-97.
    16. Lau, F. Din-Houn & Gandy, Axel, 2014. "RMCMC: A system for updating Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 99-110.
    17. Ramis Khabibullin & Sergei Seleznev, 2022. "Fast Estimation of Bayesian State Space Models Using Amortized Simulation-Based Inference," Papers 2210.07154, arXiv.org.
    18. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.
    19. Crucinio, Francesca R. & Johansen, Adam M., 2023. "Properties of marginal sequential Monte Carlo methods," Statistics & Probability Letters, Elsevier, vol. 203(C).
    20. Rutger Jan Lange, 2020. "Bellman filtering for state-space models," Tinbergen Institute Discussion Papers 20-052/III, Tinbergen Institute, revised 19 May 2021.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9511-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.