Probability Theory and Bayesian Networks

Aim

The course gives an introduction to the analysis of causal networks. It discusses graphical modelling and algorithms for updating the probability distributions. The student should expect to acquire some basic knowledge of the theory and engineering applications of Bayesian networks. By the end of the course, the student will have:

• encountered the Bayesian paradigm.
• seen the definition of a Bayesian Network.
• seen some applications of Bayesian networks in engineering.
• understood various graphical representations of conditional independence and how to use them for efficient updating.
• learned how to construct a junction tree and how to pass messages along a junction tree to update the probability distribution over the network.
• have encountered Pearl's intervention calculus.

Content

• Uncertainty and the Bayesian Paradigm, Jeffrey's and Pearl's update methods, multinomial sampling and the Dirichlet distribution.
• Conditional independence and d-separation, Bayesian Networks.
• Hard, soft and virtual evidence, Bayesian sufficient statistics, Markov chain Monte Carlo methods
• Decomposable graphs, junction trees, Markov equivalence, the essential graph and chain graphs.
• Learning the conditional probability potentials.
• Learning the graph structure.
• Parameters and sensitivity; measuring distances between probability distributions.
• Graphical models and exponential families; conditional Gaussian distributions.
• Causality and Pearl's intervention calculus.
• The junction tree and message passing algorithms for probability updating.
• Factor graphs and the sum product algorithm.