(Tutorial)
This tutorial shows you how the table generator functionality can be used to simplify how tables are specified for discrete chance nodes.

Imagine you are playing a game of dice where you roll a number of dice ranging from 1 to 5. The more sixes you roll the better, so you are very interested in predicting how many sixes you can expect to roll.

A very simple Bayesian network can model your situation. Figure 1 shows a Bayesian network where the number of the dice rolled (nDice) has an impact on the number of sixes rolled (nSixes).

Figure 1: BN modelling the dice problem

nDice has states: 1, 2, 3, 4, 5 (the number of dice you could be asked to roll). nSixes has states: 0, 1, 2, 3, 4, 5 (one more than nDice since it is possible not to roll any sixes).

Now, because we want the states of the nodes to represent numeric values, we change their type to "Numbered". Here is shown how to change nDice to a numbered node:

• Select nDice with the mouse cursor
• Select the "Node Properties" item of the "Edit" menu
• Select the "Node" tab (if it is not already selected)
• From the "Type" drop down box select "Numbered"
• Click "OK"

Now, change nSixes to be numbered too!

You can edit the number of states and the state values in the left most column of the node edit pane (as you probably did in the first tutorial ). However, you can also do it through the Node Properties dialog:

• Select nDice with the mouse cursor
• Select the "Node Properties" item of the "Edit" menu
• Select the "States" tab
• Click the first state (the only state if you haven't added any states) in the states list
• Start typing "1" - this should transfer focus to the edit box below the states list
• Press the "Rename" button in the button list on the right
• Click in the edit box and type "2"
• Press the "Add After" button
• Continue entering the state values (now, pressing the enter key after typing a state value should automatically use the "Add After" button since this was the last one activated in the button list)
• After typing all states, press "OK"

Now, do the same for nSixes (remember to start with state "0").

Figure 2 shows the Node Properties dialog after having entered the state values of nDice.

Figure 2: Entering the state values of nDice

The conditional probability table of nSixes in the node edit pane should now look as the one shown in figure 3.

Figure 3: The conditional probability table of nSixes

This table is rather big and if you should fill it in yourself it would be a pretty hard task. You would also have a tool for calculating the Binomial distribution, since the probability of rolling a specific number of is a Binomial distribution depending on the number of dice you roll.

However, the Hugin GUI allows you to generate the table automatically from an expression you specify. To do this for the nSixes node follow these steps:

• Select nSixes as the currently selected node (so that it appears in the node edit pane)
• From the "Table" menu select "Expressions" (notice, that the look of the table changes dramatically - only one cell is now shown)
• Click in the single field of the table of nSixes
• From the "Table" menu select "Build Expression". This should open the "Expression Builder" dialog
• In the "Function Category" list select "Discrete Distributions" and in the "Function Name" list choose "Binomial", then press "OK". This should close the first dialog of the expression builder and open another one prompting you for the arguments to the Binomial distribution
• Click inside the edit box of the "n" argument
• Select nDice in the "Parents" list in the bottom and press "Insert"
• In the edit box of the "p" argument type "1/6"
• Press "OK"

Now, you should have the expression "Binomial (nDice, 1/6)" in the single field of the nSixes table. This is shown in figure 4.

Figure 4: The expression table of nSixes after having specified a Binomial distribution depending on nDice

This ends the tutorial of building a small Bayesian network using the table generator. Try compiling it and play with it (try selecting different values for the nDice node and propagate. After having compiled the network, you can also go back to edit mode and take a look at the generated table: Select the nSixes node and from the "Table" menu select "Manual". You will be warned that you are destroying the expression, but that does not matter now. You can rebuild them if you want.