Interpreting a Network Diagram
One of the great advantages of Bayesian Network based technologies is that they offer intuitively understandable network models. Knowing how to interpret these assists in understanding the mathematics behind the model and hence in building the confidence of the user in the output of the model, in permitting the user to use to model as an aid to reasoning, and in permitting the user to compare the results of the model with their intuition and/or knowledge of the domain.
On this page we will go through the elements that form the networks used in Inatas software and how they should be interpreted.
- Annotated Network Diagram
- Bayesian Edges
- Information Edges
- Chance Nodes
- Chance Information Nodes
- Prediction Nodes
- Prediction Information Nodes
- Decision Nodes
- Information Nodes
- Utility Nodes
Annotated Network Diagram
Bayesian edges encode the conditional independencies found in the system being modeled. Technically, the lack of an edge between two nodes represents a conditional independency holding between the two variables given those variables which d-seperate them. It is easiest to think of conditional independence in terms of information: When the variables that d-seperate two conditionally independent variables are known, there is no additional information to be had about the state of one from knowledge about the state of the other.
In practice, it is simplest to think of the presence of an edge as indicating that the variables linked are directly related. Lack of an edge indicates that they are only indirectly related, and information about the state of one is irrelevant to knowledge of the state of the other when the d-seperating variables are known.
Bayesian edges are also used to indicate the variables involved in a utility function - see the explanation of utility nodes.
Information edges encode the temporal order in which variables which may currently be unknown will come to be known relative to any decisions (represented by decision nodes) that are to be taken. In Inatas software, they only appear when a node connected to such edges is selected in the Network Display window.
When a green information edge appears between a non-decision node and a decision node, this indicates that the non-decision node will be known before the decision is made but after any decisions that occur before this decision.
When a green information edge appears between two decision nodes, this indicates that the non-selected decision node will be known before the decision represented by the selected decision node is made.
When an orange information edge appears between two decision nodes, this indicates that the selected decision node will be known before the decision represented by the non-selected decision node is made.
A chance node represents a variable that is neither under the user's control nor one which the user is interested in predicting for its own sake.
Chance Information Nodes
A prediction node represents a variable whose value the network user wants to predict. The network will evaluate the a posteriori probability distribution of a prediction variable in each provided case (set of evidence) and store it in the action results. Furthermore, for each case the network will always provide a classification of prediction variables, as specified by an actions settings.
Prediction Information Nodes
A decision node represents a variable under the network user's control. Rather than being set by nature as chance variables are, the network user can choose the value the variable takes. The use of decision variables requires the specification of utilities - represented by utility nodes. Given such utilities the network will specify a decision policy for each relevant decision variable for each possible combinations of value for all information variables relevant to that decision.
A decision variable is relevant if it is not conditionally independent of at least one node that is a parent to a utility node given nodes that represent known variables. An information variable is relevant to a given decision if it is known prior to that decision and is not conditionally independent of the node that represents that decision given nodes that represent known variables.
A decision node is always an information node.
An information node represents a variable that is either a decision or a variable which, if it is not currently known, will be known before at least one decision is made. Information nodes are temporally ordered. This order is represented by information edges.
A utility node represents a utility function which assigns a real number to all value combinations of a set of variables. These real numbers represent the utility to the network's user of these variables taking given values.
The variables whose value combinations constitute the utility functions domain are represented as the parents of the utility node in the network diagram.