Finn Verner Jensen

Aalborg University

Mathematically a Bayesian network is a graphical representation of the joint probability distribution for a set of discrete variables. The representation consists of a directed acyclic graph and to each variable A is attached the conditional probability of A given the parents of A. The joint probability distribution of all variables is then the product of all attached conditional probailities.

The graphical representation makes Bayesian networks a flexible tool for constructing models of causal impact between events – in particular when the causal impact has a random nature. Also, specification of probabilities is focussed to very small parts of the model (a variable and its parents). Having constructed the model, it can be used to compute effects of information as well as interventions. That is, the state of some variables are fixed, and the posterior probability distributions for the remaining variables are computed. Algorithms are developed for probability updating, and they perform very efficiently on a large variety of models. This makes Bayesian networks well suited for forecasting and diagnosing.

An influence diagram was originally a compact representation of a decision tree for a symmetric decision scenario: You are faced with a specific sequence of decisions, and between each decision you observe a specific set of variables. Now-a-days, an influence diagram is a Bayesian network extended with utility functions and with variables representing decisions. An influence diagram is solved by computing a strategy yielding the highest expected utility. A strategy is a set of functions; to each decision variable is specified a function which from the relevant past returns a decision. The algorithms for probability updating can be modified to solving influence diagrams.

The tutorial will through various examples introduce the basic concepts and illustrate how Bayesian networsk and influence diagrams can be used. Also, the underlying algorithms are sketched.