Bayesian Networks

A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. The term "Bayesian networks" was coined by Pearl (1985) to emphasize three aspects:

1. The often subjective nature of the input information.
2. The reliance on Bayes's conditioning as the basis for updating information.
3. The distinction between causal and evidential modes of reasoning, which underscores Thomas Bayes's posthumous paper of 1763.^[1]

Formally, Bayesian networks are directed acyclic graphs whose nodes represent variables, and whose arcs encode conditional independencies between the variables. Nodes can represent any kind of variable, be it a measured parameter, a latent variable or a hypothesis. They are not restricted to representing random variables, which represents another "Bayesian" aspect of a Bayesian network. Efficient algorithms exist that perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (such as for example speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams.

Bayesian Networks are becoming an increasingly important area for research and application in the entire field of Artificial Intelligence. This paper explores the nature and implications for Bayesian Networks beginning with an n overview and comparison of inferential statistics and Bayes’ theorem. The nature, relevance and applicability for Bayesian Network theories for advanced computability form the core of the current discussion.

A number of current applications using Bayesian networks are examined. The paper concludes with a brief description of the appropriateness and limitations of Bayesian networks for human-computer interactions and automated learning.