Electronic Journal of Statistics

Online data processing: Comparison of Bayesian regularized particle filters

Roberto Casarin and Jean-Michel Marin

Full-text: Open access

Abstract

The aim of this paper is to compare three regularized particle filters in an online data processing context. We carry out the comparison in terms of hidden states filtering and parameter estimation, considering a Bayesian paradigm and a univariate Stochastic Volatility (SV) model. We discuss the use of an improper prior distribution in the initialization of the filtering procedure and show that the regularized Auxiliary Particle Filter (APF) outperforms the regularized Sequential Importance Sampling (SIS) and the regularized Sampling Importance Resampling (SIR).

Article information

Source
Electron. J. Statist., Volume 3 (2009), 239-258.

Dates
First available in Project Euclid: 14 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1239716413

Digital Object Identifier
doi:10.1214/08-EJS256

Mathematical Reviews number (MathSciNet)
MR2495838

Zentralblatt MATH identifier
1267.65008

Subjects
Primary: 65C60: Computational problems in statistics

Keywords
Online data processing Bayesian estimation regularized particle filters Stochastic Volatility models

Citation

Casarin, Roberto; Marin, Jean-Michel. Online data processing: Comparison of Bayesian regularized particle filters. Electron. J. Statist. 3 (2009), 239--258. doi:10.1214/08-EJS256. https://projecteuclid.org/euclid.ejs/1239716413


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References

  • Andrieu, C. and Doucet, A. (2003). Online expectation–maximization type algorithms for parameter estimation in general state space models., Proc. IEEE ICASSP, 6:VI–69–VI–72.
  • Arulampalam, S., Maskell, S., Gordon, N., and Clapp, T. (2001). A tutorial on particle filters for on-line nonlinear/non-gaussian bayesian tracking. Technical Report, QinetiQ Ltd., DSTO, Cambridge.
  • Berzuini, C. and Gilks, W. (2001). Following a moving average Monte Carlo inference for dynamic Bayesian models., Journal of the Royal Statistical Society, B, 63:127–146.
  • Carter, C. and Kohn, R. (1994). On Gibbs Sampling for State Space Models., Biometrika, 81(3):541–553.
  • Celeux, G., Marin, J.-M., and Robert, C. (2006). Iterated importance sampling in missing data problems., Computational Statistics and Data Analysis, 50(12):3386–3404.
  • Chen, Z. and Haykin, S. (2002). On different facets of regularization theory., Neural Comput., 14:2791–2846.
  • Crisan, D. and Doucet, A. (2000). Convergence of sequential monte carlo methods. Technical Report N. 381, CUED-F-INFENG.
  • Djuric, P.M., Kotecha, J., Esteve, F., and Perret, E. (2002). Sequential parameter estimation of time-varying non-gaussian autoregressive processes., EURASIP Journal on Applied Signal Processing, 8:865–875.
  • Doucet, A., de Freitas, N., and Gordon, N. (2001)., Sequential Monte Carlo Methods in Practice. Springer-Verlag.
  • Doucet, A., Godsill, S., and Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering., Statistics and Computing, 10:197–208.
  • Doucet, A. and Tadic, C. (2003). Parameter estimation in general state-space models using particle methods., Annals of the Institute of Statistical Mathematics, 55(2):409–422.
  • Fearnhead, P. (2002). MCMC, sufficient statistics and particle filter., Journal of Computational and Graphical Statistics, 11:848–862.
  • Gordon, N., Salmond, D., and Smith, A.F.M. (1993). Novel approach to nonlinear and nongaussian bayesian state estimation., IEE Proceedings-F, 140:107–113.
  • Hamilton, J. (1994)., Time Series Analysis. Princeton University Press.
  • Hamilton, J.D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle., Econometrica, 57:357–384.
  • Harrison, J. and West, M. (1989)., Bayesian Forecasting and Dynamic Models. Springer-Verlag, 2 edition.
  • Harvey, A. (1989)., Forecasting, structural time series models and the Kalman filter. Cambridge University Press.
  • Kalman, R. (1960). A new approach to linear filtering and prediction problems., Transaction of the ASME, Journal of Basic Engineering, Series D, 82:35–45.
  • Kalman, R. and Bucy, R. (1960). New results in linear filtering and prediction problems., Transaction of the ASME, Journal of Basic Engineering, Series D, 83:95–108.
  • Kitagawa, G. (1998). A self-organized state-space model., Journal of the American Statistical Association, 93(443):1203–1215.
  • Liu, J. and Chen, R. (1998). Sequential Monte Carlo methods for dynamical system., Journal of the American Statistical Association, 93:1032–1044.
  • Liu, J. and West, M. (2001). Combined parameter and state estimation in simulation based filtering. In Doucet, A., de Freitas, N., and Gordon, N., editors, Sequential Monte Carlo Methods in Practice. Springer-Verlag.
  • Maybeck, P. (1982)., Stochastic Models, Estimation and Control, volume 1-3. Academic Press.
  • Musso, C., Oudjane, N., and Legland, F. (2001). Improving regularised particle filters. In Doucet, A., de Freitas, N., and Gordon, N., editors, Sequential Monte Carlo Methods in Practice. Springer-Verlag.
  • Oudjane, N. (2000). Stabilité et approximation particulaires en filtrage non-linéaire. Application au pistage. Thèse du Doctorat en Science, Université de, Rennes.
  • Pitt, M. and Shephard, N. (1999). Filtering via Simulation: Auxiliary Particle Filters., Journal of the American Statistical Association, 94(446):590–599.
  • Polson, N.G., Stroud, J.R., and Müller, P. (2002). Practical Filtering with sequential parameter learning. Tech. report, Graduate School of Business, University of, Chicago.
  • Rossi, V. (2004). Filtrage non linéaire par noyaux de convolution. Application à un procédé de dépollution biologique. Thèse du Doctorat en Science, École Nationale Supérieure Agronomique de, Montpellier.
  • Shephard, N. and Pitt, M. (1997). Likelihood Analysis of Non-Gaussian Measurement Time Series., Biometrika, 84:653–667.
  • Storvik, G. (2002). Particle filters for state space models with the presence of unknown static parameters., IEEE Transactions on Signal Processing, 50:281–289.
  • West, M. (1992). Mixture models, Monte Carlo, Bayesian updating and dynamic models., Computer Science and Statistics, 24:325–333.
  • West, M. (1993). Approximating posterior distribution by mixtures., Journal of the Royal Statistical Society, B, 55:409–442.