Bayesian Belief Networks



Bayesian belief networks (Bbns) are commonly used to model domains containing some degree of uncertainty. This uncertainty can be due to imperfect understanding or incomplete knowledge of the state of the domain, randomness in the mechanisms governing the behaviour of the domain, or a combination of these. Until recently their use has been mainly restricted to the fields of medicine and artificial intelligence. However, recent advances in computer speed and memory means that complex domains such as those represented by the environment can now be simulated. There are a number of commercially available software packages such as Hugin and Netica, which enable networks to be constructed using standard desk top PCs.
A network consists of a series of nodes, representing random variables, which interact with each other. These interactions are expressed as links between variables. An example network representing a river basin system, is shown here. The boxes are network variables, which represent the most important factors controlling the water resource status. They are linked together so that a change in one will result in a chain reaction of impacts on all the linked variables. A Bayesian belief network consists of a series of nodes, representing random variables, which interact with each other. These interactions are expressed as links between variables. Networks are described as acyclic, because these links are not permitted to form a closed loop. A node representing variable ‘A’ will be linked to a number of ‘parent’ nodes B1, B2, ….. Bn, on which it is dependent. The links or ‘edges’ are expressed as probabilistic dependencies, which are quantified through a set of conditional probability tables (CPTs). For each variable the tables express the probability of that variable being in a particular state, given the states of its parents. As more data or knowledge becomes available these tables are updated, and the associated uncertainties are reduced. For variables without parents, an unconditional distribution is defined.