Directed Acyclic Graph

• According to Wolfram Mathworld, a well-respected online repository of information on mathematics, a directed acyclic graph---also called an acyclic digraph---is a directed graph lacking cycles. In its most basic form, a directed acylic graph looks like a dot-to-dot picture, with dots representing "nodes" (information pieces) and lines between the nodes representing which direction the information flows. Arrows are placed on the lines to show the flow of data.
  
  

Consistency and Completeness

• According to professor Pearl, it's important not to overload the graph with unnecessary data because of the possibility of too many conclusions to draw from. It's also vital that the graph be as complete as possible. For example, a graph may be drawn to represent a physician's decision-making process. If a patient arrives at the doctor's office with a headache, the doctor will make a diagnosis based on how the patient presents, plus he may make a decision to run further tests. The graph must show the decision to test or not test, with clear instructions for these decisions. In addition, the graph must include every possibility for headache outcomes (including migraine, brain tumor, sinusitis and a whole host of other diseases). Without every possibility, the patient's condition could remain undiagnosed.
  
  

Modeling Human Decision Making

• Studies have shown that modeling human decisions with Bayesian networks isn't as easy as it first appears. Professor Pearl states that because human reasoning is subjective and incomplete, it would seem reasonable to start with probability theory to design a graph. However, this basic modeling process does not include the more complex pieces of human reasoning; if we were to attempt to construct a probability table for some complex decisions made by people, it would take a computer an extraordinary amount of time to compute what it would take a person a split-second to decide.
  
  

Advantages

• According to Microsoft, Bayesian networks are useful for data modeling because they can handle decision making even when some variables are missing. Bayesian networks can represent causal relationship, include prior knowledge and predict possible outcomes with ease.
  
  

Applications

• Jir Vomlel of the Institute of Information Theory and Automation Academy of Sciences of the Czech Republic states that Bayesian networks can be used to represent a wide variety of decision-making processes in the real world, including medical diagnostics, decision making maximizing expected utility, adaptive testing and decision-theoretic troubleshooting.