Propagation of Evidence Using Junction Tree in Bayesian Networks

Öz

A Bayesian network is directed a cyclic graphs in which the nodes represent variables and the edges signify direct dependencies between variables. The strenghts of these edges dependencies are defined by conditional probabilities. In Bayesian networks, the evidence propagation is introduced by junction tree algorithm. Finally, strenghts of conditional probabilities are calculated by using application data and then the probabilities are examined. Here, SPSS software is used to constitute contingency tables and HUGIN software for probability calculus.

Anahtar Kelimeler

• Bayesian Nerworks
• Conditional Independence
• Conditional Probability
• Function Tree

Bayes Ağlarda Birleşme Ağaçlarını Kullanarak Olayların Genişlemesi

Öz

Bir Bayes ağ, yön verilmiş döngüsel olmayan bir grafiktir. Bu grafikte, düğümler rastgele değişkenleri gösterir ve kenarlar değişkenler arası doğrudan bağımlılıkları tanımlar. Kenarlar arası bağımlılıkların gücü, koşullu olasılıklar ile tanımlanmıştır. Bayes ağlarda, olayların genişlemesi, birleşme ağacı algoritması ile tanıtılmıştır. Uygulamada yer alan veriden hareketle, koşullu olasılıklar hesaplanmış ve bu olasılıklar incelenmiştir. Burada, olumsallık tabloların oluşturulması için SPSS 8.0 paket programı ve olasılık hesaplamaları için de HUGIN paket programı kullanılmıştır.

Anahtar Kelimeler

• Bayes Ağlar
• Birleşme Ağacı
• Koşullu Bağımsızlık
• Koşullu Olasılık

Kaynakça

1. COWELL, R.G., (1999), Inroduction to Inference in Bayesian Networks, in Learning in Graphical Models, 9-26.
2. EDWARDS, D., (1995), Introduction to Graphical Modelling, Springler Verlag, New York.
3. FRIEDMAN, N. and GOLDSZMIDT, M., (1996), Learning Bayesian Networks with Local Structure, Proceedings 12th Conference on Uncertainty in Artificial Intelligence, IFI-95-03109, 421-459.
4. HILL, D. A., DELANEY, L. M., RONCAL, S., (1997), a Chi-Square Automatic ınteraction Detection, (CHAlD) Analysis of Factors Determining Trauma Outcomes, Journal of Trauma-Injury Infection and Critical Core, Vol. 42, ISS 1,62-66.
5. HUGIN SYSTEMS, (1998), Introduction to the HUGIN System, HUGIN Expert Ltd., htttp://www.hugin.dk.
6. JENSEN, F.V., (1996), An Introduction to Bayesian Networks, UCL Press Ltd., London.
7. JENSEN, F.V., OLESEN, K.G. AND ANDERSEN, S.K., (1990), an Algebra of Bayesian Belief Universes for Knowledge-Based Systems, Networks, Vol. 20, 637-659.
8. LAURITZEN, S.L., (1996), Graphical Models, Oxford University Press, Oxford.

9. LAURITZEN, S.L. and SPIEGELHALTER, D.J., (1988), Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems, J.R. Statist. Soc. B, 50(2), 157-224.
10. LIAROKAPIS, D., (1999), An Introduction to Belief Networks, http://www.cs.umb.edu/dimitris.
11. NlEDERMAYER, D., (l998), An Introduction to Bayesian Networks and Their Contemporary Applications, http://www.gpfn.sk.ca/-daryle/papers/ bayesian_networks/bayes html.
12. PEARL, J., (1986), Fusion, Propagation and Structuring in Belief Networks, Artificial Intelligence, 29, 241-288.
13. SPIEGELHALTER, DJ., DAWlD, A.P, LAURITZEN, S.L. AND COWELL, R.G., (1993), Bayesian Analysis in Expert Systems. Statistical Science, Yol.8, No.3, 219-283.
14. SPIEGELHALTER, D.J. and LAURITZEN, S.L., (1990), Sequetial Updating of Conditional Probabilities on Directed Graphical Structures, Networks, 20, 579-605.
15. STEPHENSON, T.A., (2000), An Introduction to Bayesian Network Theory and Usage, IDlAP Research Report 00-03.
16. TÜRKİYE İSTATİSTİK YILLIĞI, (1996), Demografi Şubesine Ait İntihar Verileri, Devlet İstatistik Enstitüsü, Ankara.