Bayesian network

A Bayesian Network is an acyclic directed weighted graph. The weights of the nodes are conditional probabilities.

Bayesian Networks are also known under the following names: bayesian belief networks, belief networks, causal probabilistic networks or knowledge maps.

• Bayesian Networks (BAN) - Presentation and introduction of BAN.
  WWW, here:04, here:05, here:06, (29.03.2006)
• Bayesian Belief Nets - Several introductions, presentations and articles
  WWW, here:Learning Belief Nets, (29.03.2006)
• Kevin Murphy - A Brief Introduction to Graphical Models and Bayesian Networks
  WWW. (1998)
• Introduction to Bayesian Networks - An Introduction to Bayesian Networks and their Contemporary Applications
  WWW (14.12.2006)
• Bayesian Network Repository - Collection of BN examples
  WWW

• Obtaining the correspondence between Bayesian and Neural Networks - A. Stassopoulou & M. Petrou
  WWW, here. (29.03.2006)
• An introduction to graphical models - Kevin Murphy
  WWW, here, (2001)
• Bayesian Networks Without Tears - Eugene Charniak
  WWW, here, (1991)
• Dynamic Bayesian Networks for Information Fusion with Applicaqtion to Human-Computer Interfaces - Vladimir Pavlovic: PhD Thesis
  WWW. here, (1999)
• Dynamic Bayesian Networks: A State of the Art V. Mihajlovic and M. Petkovic
  WWW. here, (2001)
• An Introduction to Bayesian and Dempster-Shafer Data Fusion - D. Koks and S. Challa.
  WWW.
• Learning Dynamic Bayesian Networks - Z. Ghahramani
  WWW (1998).
• A Dynamic Bayesian Network Approach to Figure Tracking - V. Pavlovic, K. Murphy, et al
  WWW (1999).
• The Centre of Gravity Network Effects Tool: Probabilistic: Modelling for Operational Planning - Lucia Falzon and Jayson Priest
  Australian DSTO, European Journal of OR (2004).
• Generating Conditional Probabilities for Bayesian Networks: Easing the Knowledge Acquisition Problem - Balaram Das
  Citebase (2004).

Surrey Papers

• Agent-Based Parsimonious Decision Support Paradigm Employing Bayesian Belief Networks - Panos Louvieris, Andreas Gregoriades, et al
  WWW abstract. (July 2005)
• Smart Decision Support System Using Parsimonious Information Fusion - Panos Louvieris, Natasha Mashanovich, et al
  WWW abstract. (July 2005)

• Hugin Expert - Commercial: GUI, API for C++,Java,...
  WWW, download, (30/03/2006)
• Bayes Net Toolbox for Matlab - Kevin Murphy's Bayes Net Toolbox
  WWW, here, (26/11/2005)
• Bayesia - Commercial: Neat designed software
  WWW
• see also Wikipedia
• see also SW Packages for graphical models and BN

• Bayesian node - represents a random variable, latent variable or hypothesis
  WWW
• Conditional Probability - P(E|F)...the probability that event E occures given that F has occured.
  WWW
• Bayes' formula - P(E) = P(E|F) P(F) + P(E|¬F)(1-P(F))
  WWW
• Inference - Computation of conditional probability given some evidence (probabilities in other nodes).
  WWW
• Learning - "To learn means to adjust the network and/or probabilities such that it describes the observed data better."
  WWW
• Hybrid Bayesian Network - A Bayesian Network with discrete and continuous variables (CPT, CPD).
  WWW

• Jensen, F. V., 2001, Bayesian Networks and Decision Graphs. Springer Verlag - best introduction book
  Amazon, Amazon UK.
• Pearl, J., 2000, Causality: Models, Reasoning, and Inference. Cambridge University Press - for causal directed acyclic graphs
  Amazon UK.
• Cowell, et al, 1999, Probabilistic Networks and Expert Systems. Springer Verlag - emphasises on exact inference
  Amazon UK.
• Kevin Murphy, 2002 Dynamic Bayesian Networks: Representation, Inference and Learning. University of California, Berkeley - PhD Thesis
  PhD Thesis.
• see also Wikipedia

• 2D area into a 3D probability surface. The following movie shows how to map a 2D triangle into a 3D probability space. Download movie.
• Dempster-Shafer theory: Wiki
• Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning (DSmT): book preview (2004) , book (2006)