Extend your BN to become a Bayesian Decision Network $($BDN$)$ that will be used to decide

when a transaction should be blocked. Use the following information: For each legitimate

transaction processed, the credit card company earns a profit of roughly $0\mathrm{.}5\%$ of the transaction$$s value through interest charges and merchant charges. For instance, on each transaction

of $$1000,$ the credit card company expects a profit of roughly $$5.$ Assuming that the credit

$2$

card company covers fraudulent transactions, it will suffer a loss equal to the value of each

fraudulent transaction. However, if a fraudulent transaction is blocked, there is no loss. In

the event where a legitimate transaction is blocked, customers get annoyed $($and sometimes

cancel their credit card$),$ which is considered to be equivalent to an expected loss of $$10.$

$($a$)$ Extend your BN to a BDN$.$ Assume transactions of $$1000.$ This network should encode

the information stated above. In addition to the six chance nodes defined in Question $1,$

your network should include a decision node and a utility node: $(10$ marks$)$

$$ B $$ decision to block $($or not$)$ a transaction.

$$ U $$ utility.

The arcs into the decision node should encode informational links, and the arcs into the

utility node should encode utility dependencies.

What to hand in:

$$ A Netica file of the BDN$,$ and a screenshot of your BDN and the utility table.

$$ An explanation of the informational link$($s$)$ and the utility dependencies.

$$ A recommendation of whether the credit card company should block a transaction in

the absence of information? Why?

$($b$)$ Validate your BDN by calculating manually the utilities of the actions. $(6$ marks$)$

What to hand in:

$$ Your calculation of the utilities of the actions.

$($c$)$ Should a $$1000$ transaction be blocked when it is a foreign transaction that wasn$$t done

over the Internet and computer related accessories were purchased in the past week? Enter

each piece of evidence in sequence and update the decision node in turn. Use

the structure of the BN and the CPTs to explain the impact of each new piece

of evidence. $(6$ marks$)$