Elements of GeNIe Diagrams: Arcs
From DSL
Arcs between nodes denote direct influences between them.
To learn how to create arcs between nodes, see Tutorial 3: Building a Bayesian Network.
One remark about editing diagrams is that GeNIe does not allow moving arcs between nodes, i.e., it is not possible to select and drag the head or the tail of an arc from one node to another. You can perform an operation like this by first deleting the original arc and then creating a new arc. These operations have serious consequences on the definitions of the nodes pointed by the heads of the arcs - deleting an arc deletes a portion of the definition of the node, adding an arc leads to a default extension of that definition. GeNIe tries to minimize the impact of adding and deleting arcs in terms of changing the conditional probability distributions. Whenever you add an arc, which amounts to adding a dimension to the child variable's conditional probability table, GeNIe will duplicate the current table, preserving the numbers from the original table. Whenever you delete an arc, which amounts to reducing a dimension of the child variable's conditional probability table, GeNIe will remove only a part of the table, preserving the rest.
Normally, an arc in a Bayesian network or an influence diagram denotes an influence, i.e., the fact that the node at the tail of the arc influences the value (or the probability distribution over the possible values) of the node at the head of the arc. These arcs are drawn as solid lines. Some arcs in influence diagrams have clearly causal meaning. In particular, a directed path from a decision node to a chance node means that the decision (i.e., a manipulation of the graph) will impact that chance node in the sense of changing its probability distribution.
Arcs coming into decision nodes have a different meaning. As decision nodes are under decision maker's control, these arcs do not denote influences but rather temporal precedence (in the sense of flow of information). The outcomes of all nodes at the tail of informational arcs will be known before the decision will need to be made. In particular, if there are multiple decision nodes, they need to be all connected by informational arcs. This reflects the fact that the decisions are made in a sequence and the outcome of each decision is known before the next decision is made. Informational arcs are drawn as dashed lines.
GeNIe displays also arcs between nodes and submodels. An arc from a node N to a submodel S means that at least one node in S depends on N. An arc from a submodel S to a node N means that N depends on at least one node in S. An arc from a submodel S1 to a submodel S2 means that there is at least one node in S2 that depends on at least one node in S1. Arcs between submodels can be double-headed, in which case the relations listed above can be reciprocal. For example, a double-headed arrow between a node N and a submodel S means that there is at least one node in S that depends on N and that there is at least one node in S that influences N. GeNIe does not show arcs that are coming from the outside of the current submodel window. Existence of arcs coming from outside the current submodel and ending in a node in the current submodel is marked by a small triangle on the left-hand side of the node. Existence of arcs originating in a node in the current submodel and ending in a higher-level submodels is marked by a small triangle on the right-hand side of the node. These links can be followed by right-clicking on the small triangles.
Whether arcs are influences or are informational, cycles in the graph, i.e., directed paths that start and end at the same point, are forbidden. GeNIe will not allow you to draw cyclic graphs. Please note that even though GeNIe will enforce the underlying graph to be acyclic, you may still be able to observe cyclic graphs involving submodel nodes. This is due to the meaning assigned to arcs between submodels.
