Hello Julian Russell, Another solution, which keeps a compact network form, is based on iterative inferences. Indeed, it is possible to compute the probability distribution of any variable at time step k+1 based on the probabilities corresponding to time step k. The probability distributions at time step k+2� are computed using successive inferences (Welch and Thelen 2000, Weber and Jouffe 2003). Then a network with only two time slices is defined this networks is called 2-TBN (Boyen and Koller 1998). The first slice contains the nodes corresponding to the current time step (k), the second one those of the following time step (k+1).
You can try using BayesiaLab ( http://www.bayesia.com/ ) this software allows 2TBN model. WEBER Philippe Ref: Boyen X. and Koller D. (1998) Tractable for Complex Stochastic Processes. Proceedings of the 14th Annual Conference on Uncertainty in AI (UAI), Madison, Wisconsin, July 1998, pages 33--42. Weber P., L. Jouffe (2003). Reliability modelling with Dynamic Bayesian Networks. 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SAFEPROCESS'03), Washington, D.C., USA, June 9-11. Welch R. and T. Thelen (2000). Dynamic reliability analysis in an operational context: the Bayesian network perspective. In Dynamic reliability: future directions. Edited by: C. Smidts, J. Devooght and P.E. Labeau, ISBN 0 9652669 3 1, Maryland, USA. Julian Russell a �crit : > There appears to be a class of problem that BN's are not designed to > solve. These are problems involving (probabilistic) simulation of two > player games where cycles are required to be followed to calculate the > probability of nodes that effectively have circular references. The > program Netica does a clever kludge by simply duplicating the whole > network for solving iterations of this kind. I suspect that there may be > other ways such as enforcing timing limitations on calculation. > > Does anybody have any other ideas on how to use a BN in the context of > 'two player games' to solve the circular reference problem? > > Regards, > Julian Russell > USQ - -- __________________________________________________ Philippe WEBER Ma�tre de Conf�rences CRAN - CNRS UMR 7039 Universit� Henri Poincar�, Nancy 1 - ESSTIN 2, rue Jean Lamour 54519 VANDOEUVRE-LES-NANCY Cedex (France) E-Mail : [EMAIL PROTECTED] t�l +33 (0)3 83 68 51 27 fax +33 (0)3 83 68 50 12 __________________________________________________ ------- End of Forwarded Message
