Abstract
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.
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References
Bayesian information criterion was derived in, G. Schwartz, “Estimating the dimension of a model”, Ann. Statist., 6 (1978) 461–464.
Akaike information criterion was due to, H. Akaike, “A new look at the statistical model identification”, IEEE Trans. Automat. Contr., AC-19 (1974) 716–723
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) 35–45
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) 444–450
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, 1995
A popular Kalman web site is http://www.cs.unc.edu/~welch/kalman , which contains and refers to tutorials, books, downloadable articles, researches, links, as well as software.
A textbook on optimal filtering is, B.D.O. Anderson and J.B. Moore, “Optimal Filtering”, Prentice-Hall, Englewood Cliffs, N.J. (1979)
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) 152–166
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. 2278–2286
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 1996
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© 2003 Springer Science+Business Media New York
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Wang, SC. (2003). Graphical Model. In: Interdisciplinary Computing in Java Programming. The Springer International Series in Engineering and Computer Science, vol 743. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0377-4_13
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DOI: https://doi.org/10.1007/978-1-4615-0377-4_13
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