bayesian network and inference
19 A bank in New Zealand has asked us to write an app that allows customers to check on the status of their credit card accounts. In particular, customers whose cards have been disabled should be able to use the software to determine why the card was disabled, and to assess which activities will likely lead to their card being disabled. A card can become disabled when the account is over its limit, when the card has expired, or when a fraud alert has occurred. Fraud alerts often occur when a card is used internationally or when the card is used at a new vendor, e.g., a store where the customer has never shopped before. We construct the following Bayesian network containing 5 atoms: 1. Alert is true if and only if the bank issues a fraud alert. 2. Limit is true if and only if the account is over its limit. 3. Expired is true if and only if the card has expired. 4. Disabled is true if and only if the card is disabled. 5. Contacted is true if and only if the bank has contacted the cardholder. Limit Alert Expired Disabled Contacted 1. Consider the following scenario: Let's say you are a cardholder and your card stops working. However, you did not get contacted by the bank. Moreover, you are sure that there is fraud alert. What are the observed variables and their values in this scenario? 2. Suppose you are sure that there is no fraud alert. The table below gives the probability distribution P(Disable | Alert, Limit, Expired). Suppose P(Limit)=0.2. Given that your card is disabled, compute the probability of your account being over its limit. Describe in detail how you solve the problem using the variable elimination algorithm and state your conclusion. Limit Expired Disabled Probability True True True True True False 0 True False True True False False False True False False False True False 0.5 True False True 0.5 1 0 0 1 False False 19 A bank in New Zealand has asked us to write an app that allows customers to check on the status of their credit card accounts. In particular, customers whose cards have been disabled should be able to use the software to determine why the card was disabled, and to assess which activities will likely lead to their card being disabled. A card can become disabled when the account is over its limit, when the card has expired, or when a fraud alert has occurred. Fraud alerts often occur when a card is used internationally or when the card is used at a new vendor, e.g., a store where the customer has never shopped before. We construct the following Bayesian network containing 5 atoms: 1. Alert is true if and only if the bank issues a fraud alert. 2. Limit is true if and only if the account is over its limit. 3. Expired is true if and only if the card has expired. 4. Disabled is true if and only if the card is disabled. 5. Contacted is true if and only if the bank has contacted the cardholder. Limit Alert Expired Disabled Contacted 1. Consider the following scenario: Let's say you are a cardholder and your card stops working. However, you did not get contacted by the bank. Moreover, you are sure that there is fraud alert. What are the observed variables and their values in this scenario? 2. Suppose you are sure that there is no fraud alert. The table below gives the probability distribution P(Disable | Alert, Limit, Expired). Suppose P(Limit)=0.2. Given that your card is disabled, compute the probability of your account being over its limit. Describe in detail how you solve the problem using the variable elimination algorithm and state your conclusion. Limit Expired Disabled Probability True True True True True False 0 True False True True False False False True False False False True False 0.5 True False True 0.5 1 0 0 1 False False
