Bayesian Networks – Practice 1 Problem 1. You have a new burglar alarm installed. It reliably detects burglary, but also responds to minor earthquakes. Two neighbors, John and Mary, promise to call the police when they hear the alarm. John always calls when he hears the alarm, but sometimes confuses the alarm with the phone ringing and calls then also. On the other hand, Mary likes loud music and sometimes doesn’t hear the alarm. Given evidence about who has and hasn’t called, you’d like to estimate the probability of a burglary (from Pearl (1988)). (Let B = burglary, E = earthquake, A = alarm, J = JohnCalls, M = MaryCalls) a. 주어진 베이지안망의 구조를 이용하여 P(A, B, E, J, M)을 확률식으로 기술하시오. b. 지진(Earthquake)이 발생했는데 알람(Alarm)이 울리지 않을 확률을 계산하시오. c. 도둑이 들었을 때(Burglary) 존이 전화할 (JohnCalls) 확률을 계산하시오. d. 존이 전화를 했는데 (JohnCalls) 도둑이 들었을(Burglary) 확률을 계산하시오. Problem 2. Metastatic cancer is a possible cause of brain tumors and is also an explanation for increased total serum calcium. In turn, either of these could explain a patient falling into a coma. Severe headache is also associated with brain tumors. (This example has a long history in the literature, namely Cooper, 1984, Pearl, 1988, Spiegelhalter, 1986.) a. Represent these causal links in a belief network. c. Give an example of an independence assumption that is implicit in this network. b. a 의 베이지안망 구조를 이용하여 joint probability 를 확률식으로 기술하시오. Problem 3. 입학 허가를 받은 학생이 실제로 등록을 할 확률이 얼마인지 계산하려고 한다. 이와 관련된 확률값을 아래 베이지안 네트워크에 표시하였다. P(A|D)의 값을 계산하라. A＝입학 허가를 받은 학생이 등록함 B＝입학 성적이 매우 좋음 C＝추천서가 매우 좋음 D＝입학 허가를 받음