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Solving a Decision Net

After creating a decision net, you can compile it in the same way as you compile a Bayes net (except the optimizing compiler doesn’t work on decision nets yet).

Netica will attach to each decision node a deterministic function (the optimal is never probabilistic), which provides a value for the decision node for each possible configuration of parent values.  Since the links into a decision node indicate what the decision maker will know when he is about to make the decision, this function provides a decision for each possible information state.  Taken together, the decision functions from each of the decision nodes form a policy which maximizes the expected value of the sum of the utility nodes.  You can use the table dialog box to examine the optimal decision table for each decision node.

To display the overall expected utility corresponding to each choice of a decision node, change the node style to belief-bars.  The numerical value will appear directly after each state name (although no bars will be drawn).  The best decision is the one with the highest expected utility.

Findings and decision node choices may be entered in the same way as for Bayes nets, and updating done to reveal the new probabilities and expected utilities.

Links Change:  When you compile a decision net, Netica may add or remove some links into decision nodes.  If a link disappears, then it means that for all possible utilities, CPTs or findings, that link won't be relevant to the decision.  If a new link appears, then it is a no-forgetting link that is relevant to the decision.

Missing Numbers:  If there is a path from one decision node to another, it means that the ancestor decision is to be made before the descendent decision.  So you must enter a choice for the ancestor decision node before utilities will be displayed at the descendent decision node (if you are familiar with Hugin, you will know that it displays utilities for the descendent decision node all the time, but the Hugin documentation states that these values are not meaningful until the ancestor decision choice is entered).

Example:  For an example of solving a decision net, see the umbrella example.

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