Graphical Model

  • Sun-Chong Wang
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 743)


Complexity in nature or biology results more from the structure of the system than from some ‘magic’ parameter values in the system. Examples are transcriptional networks of genes and the Internet, both of which are resilient to random attacks. Network structures have been studied by graphical models.


Global Position System State Vector Kalman Filter Graphical Model Stock Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bayesian information criterion was derived in, G. Schwartz, “Estimating the dimension of a model”, Ann. Statist., 6 (1978) 461–464.MathSciNetCrossRefGoogle Scholar
  2. Akaike information criterion was due to, H. Akaike, “A new look at the statistical model identification”, IEEE Trans. Automat. Contr., AC-19 (1974) 716–723MathSciNetCrossRefGoogle Scholar
  3. The Kalman method was first proposed in, R.E. Kalman, “A New Approach to Linear Filtering and Predicting Problems”, Transaction of the ASME-Journal of Basic Engineering, 82 (Series D) (1960) 35–45CrossRefGoogle Scholar
  4. For the Kalman formulas, we have followed the notation of, R. Fruhwirth, “Application of Kalman Filtering to Track and Vertex Fitting”, Nucl. Instr. & Methods, A262 (1987) 444–450CrossRefGoogle Scholar
  5. A tutorial derivation of the Kalman filter can be found in the downloadable article, A.L. Barker, D.E. Brown, and W.N. Martin, “Bayesian Estimation and the Kalman Filter”, IPC-TR-94–002, Revised Sept. 19, 1994. Its published version appears in, Computers and Mathematics with Applications, Vol. 30, No. 10, 1995Google Scholar
  6. A popular Kalman web site is , which contains and refers to tutorials, books, downloadable articles, researches, links, as well as software.
  7. A textbook on optimal filtering is, B.D.O. Anderson and J.B. Moore, “Optimal Filtering”, Prentice-Hall, Englewood Cliffs, N.J. (1979)zbMATHGoogle Scholar
  8. Solutions to the H infinity problem are shown in, K.M. Nagpal and P.P. Khargonekar, “Filtering and Smoothing in an H Setting”, IEEE Trans. Automat. Contr., AC-36, (1991) 152–166MathSciNetCrossRefGoogle Scholar
  9. A review of H infinity filters is, U. Shaked and Y. Theodor, “H-Optimal Estimation: A Tutorial”, Proceedings of the 31st Conference on Decision and Control, Tucson, Arizona, December 1992, pp. 2278–2286Google Scholar
  10. A useful thesis with examples on H infinity is, K. Takaba, “Studies on H Filtering Problems for Linear Discrete-Time Systems”, doctoral dissertation in Applied Mathematics and Physics, Kyoto University, January 1996Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Sun-Chong Wang
    • 1
  1. 1.TRIUMFCanada

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