Skip to main content

‘Unobserved’ Monte Carlo Methods for Adaptive Algorithms

  • Chapter
  • 2165 Accesses

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 46))

Abstract

Many Signal Processing and Control problems are complicated by the presence of unobserved variables. Even in linear settings this can cause problems in constructing adaptive parameter estimators. In previous work the author investigated the possibility of developing an on-line version of so-called Markov Chain Monte Carlo methods for solving these kinds of problems. In this article we present a new and simpler approach to the same group of problems based on direct simulation of unobserved variables.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Benveniste, A., M. Metivier, and P. Priouret. (1990). Adaptive Algorithms and stochastic approximations. Springer-Verlag, New York.

    Book  Google Scholar 

  • Dempster, A.P., N.M. Laird, and D.B. Rubin. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B, 39:p.1–38.

    MathSciNet  MATH  Google Scholar 

  • Geman, S. and D. Geman. (1984). Stochastic relaxation, gibbs distributions and the bayesian restoration of images. IEEE. Trans. Patt. Anal. Machine Intell., 6:721–741.

    Article  Google Scholar 

  • Kanatani, K. (1996). Statistical optimization for Geometric Computation: Theory and Practice. North-Holland, Amsterdam.

    MATH  Google Scholar 

  • Kuk, A.Y.C., and Y. W. Cheng. (1997). The Monte Carlo Newton Raphson algorithm. Jl Stat Computation Simul.

    Google Scholar 

  • Kitagawa, G. (1998). Self organising state space model. Jl. Amer. Stat. Assoc, 93:1203–1215.

    Google Scholar 

  • Kushner, H.J. (1984). Approximation and weak convergence methods for random processes with application to stochastic system theory. MIT Press, Cambridge MA.

    MATH  Google Scholar 

  • Ljung, L. (1983). Theory and practice of recursive identification. MIT Press, Cambridge, Massachusetts.

    MATH  Google Scholar 

  • Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. (1953). Equations of state calculations by fast computing machines. J. Chem. Phys., 21:1087–1091.

    Article  Google Scholar 

  • Ng, L. and V. Solo. (2001). Errors-in-variables modelling in optical flow estimation. IEEE Trans. Im.Proc., to appear.

    Google Scholar 

  • Neuman, S.P. and S. Yakowitz. (1979). A statistical approach to the inverse problem of aquifer hydrology, I. Water Resour Res, 15:845–860.

    Article  Google Scholar 

  • Rappaport, T.S. (1996). Wireless Communication. Prentice Hall, New York.

    Google Scholar 

  • Ripley, B.D. (1996). Pattern recognition and Neural networks. Cambridge University Press, Cambridge UK.

    Book  Google Scholar 

  • Roberts, G.O. and J.S. Rosenthal. (1998). Markov chain monte carlo: Some practical implications of theoretical results. Canadian Jl. Stat., 26:5–31.

    Article  MathSciNet  Google Scholar 

  • Sastry, S. and M. Bodson. (1989). Adaptive Control. Prentice Hall, New York.

    MATH  Google Scholar 

  • Solo, V. and X. Kong. (1995). Adaptive Signal Processing Algorithms. Prentice Hall, New Jersey.

    Google Scholar 

  • Solo, V. (1999). Adaptive algorithms and Markov chain Monte Carlo methods. In Proc. IEEE Conf Decision Control 1999, Phoenix, Arizona, IEEE.

    Google Scholar 

  • Solo, V. (2000a). ‘Unobserved’ Monte Carlo method for system identification of partially observed nonlinear state space systems, Part I: Analog observations. In Proc JSM2001, Atlanta, Georgia, August, page to appear. Am Stat Assocn.

    Google Scholar 

  • Solo, V. (2000b). ‘Unobserved’ Monte Carlo method for system identification of partially observed nonlinear state space systems, Part II: Counting process observations. In Proc 39th IEEE CDC, Sydney Australia. IEEE.

    Google Scholar 

  • Tekalp, M. (1995). Digital Video Processing. Prentice-Hall, Englewood Cliffs, N.J.

    Google Scholar 

  • Wei, G.C.G. and M. Tanner. (1990). A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms. Jl. Amer. Stat. Assoc, 85:699–704.

    Article  Google Scholar 

  • Yakowitz, S. (1969). Mathematics of Adaptive Control Processes. Elsevier, New York.

    MATH  Google Scholar 

  • Yakowitz, S. (1985). Nonparametric density estimation, prediction and regression for Markov sequences. Jl. Amer. Stat. Assoc, 80:215–221.

    Article  MathSciNet  Google Scholar 

  • Yakowitz, S. and F. Szidarovszky. (1984). A comparison of kriging with nonparametric regression methods. Jl Mult Anal.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science + Business Media, Inc.

About this chapter

Cite this chapter

Solo, V. (2002). ‘Unobserved’ Monte Carlo Methods for Adaptive Algorithms. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, New York, NY. https://doi.org/10.1007/0-306-48102-2_18

Download citation

Publish with us

Policies and ethics