FIT5047 Semester 1, 2017 Bayesian Networks Laboratory FIT5047 { Bayesian Networks Laboratory (7.5%) Question 1: Bayesian Networks, Netica ( 12 + 1  4 + 2  2 + 3 + 1  10 + 7 = 40 marks ) Expand the Bayes Net you developed in the BN tutorial (available on moodle under the name SmokeAlarm.dne ) to include three more events: Smoke (you can see smoke in your apartment), Evacuation (your apartment building is evacuated), and Report (the local newspaper writes a report about the evacuation of your apartment). The probability of smoke when there is re is 0.9, the probability of smoke when there is no re is 0.01. When your apartment building has a re alarm, there is a 0.88 probability that there will be an evacuation, but there is never an evacuation when there is no re alarm. If there is an evacuation, there is a 0.75 probability that the newspaper will write a report on it, and if there is no evacuation there is a 0.99 probability that the newspaper won't report it. (a) Add the necessary nodes and edges to your BN, and input the corresponding conditional probability tables. Justify your expanded network and CPTs. A BN without justica- tion will receive no marks. (b) Use Netica on the expanded BN to answer the following questions: i. What is the marginal probability that your smoke detector has been tampered with? ii. What is the marginal probability that there will be a news report tomorrow? iii. Let's assume that you have observed that there is smoke in your apartment. What is the posterior probability that there will be a news report tomorrow? iv. Let's assume that you have observed that there was no re, and that there was a news report about your apartment. What is the posterior probability that your smoke detector has been tampered with? v. Let's assume that you have observed that there is no smoke in your apartment. What is the posterior probability that your smoke detector has been tampered with? What conditional independence property could help you here? vi. Let's assume that you have observed that there has been a news report about your apartment, and there is no smoke in your apartment. What is the posterior probability that your smoke detector has been tampered with? Given that the news report was observed, why does observing the absence of smoke aect your belief of whether or not your smoke alarm was tampered with? vii. Let's assume that you have observed that there was no re, that there was a news report about your apartment, and that there is smoke in your apartment. What is the posterior probability that your smoke detector has been tampered with? How does observing whether or not there is smoke aect your belief of whether or not your smoke detector has been tampered with? Why? 1