Figure 1 shows the joint analysis pane appearing after activating the joint configurations dialog. In this pane the joint probability distribution over a set of nodes is shown (Figure 3). The set of nodes in the joint can be defined by selecting the "Variables" tab (Figure 2).
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Figure 1: No joint distribution has been computed. |
A joint probability distribution is computed over a set of nodes. The set of nodes can be selected as indicated in Figure 2.
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Figure 2: Selecting the set of nodes in the joint distribution. |
Selecting nodes to appear in the joint proceeds in the same way as selecting Target(s) of Instantiations in the d-Separation pane.
After selecting the set of nodes their joint probability distribution is computed by selecting Perform. The results for the example are shown below in Figure 3 where the probabilities are sorted.
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Figure 3: The joint distribution over the selected set of nodes. |
The joint probability distribution over a set of nodes is computed by message passing in a junction tree. The feasibility of computing a joint distribution is in part determined by the size of the junction tree and the combined state space size of the nodes in the joint. The size of the joint distribution is equal to the product of the state space sizes of the nodes in the jiont. Thus, the size of the joint distribution grows exponentially with the number of nodes in the joint.
Notice that the "m-most" probable configurations can be identified by sorting the rightmost column. This do, however, require that the full joint is computed.