If We Observe Alarm True Are Burglary And Earthquake Independent, If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Given the following Bayes Network (b - Burglary, e - earthquake, a - alarm, j - JohnCalls, m - MaryCalls): And the following expanded expression for the query (a - normalization constant): What is be the Burglars and Earthquakes You are at a “Done with the AI class” party. 4 Consider the Bayesian network shown in the figure. Consider the Bayesian network in the image attached. We assume a small probability f of a false alarm caused by some other event. 2 (included above). [10 pts] Bayesian Network: Independence a) [5 pt] If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. , P (B, E) = P (B) * P (E). Figure 9: The Bayesian network for the burglar alarm example. John has two neighbors, David and Sophia, who would inform John Modified Book Problem 14. If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of condi- tional independence [1]. Wn I have a burglar alarm that is sometimes set off by minor earthquakes. Sometimes your alarm is set off by minor We need to multiply the individual probabilities of burglary, the alarm sounding given burglary but no earthquake and neither David nor Sophia calling Harry. Burglars and Earthquakes You are at a “Done with the AI class” party. Modified Book Problem 14. We will also assume that Jacob's call and Mark's call are conditionally JohnCalls Alarm Earthquake MaryCalls Computation of the probabilities of several different event combinations of the Burglary-Alarm belief network example: If we observe “Alarm is True”, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Question: Consider the Bayesian network in Figure 14. The document defines a Bayesian network model to analyze the probabilities in a burglary alarm example. If we observe A larm = true, are Burglary and Earthquake independent? Justify yoer answer by calculating whether the probabilities involved satisfy the definition of conditional independence. If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. 2.  If we observe Alarm = true, are Burglary and a) If no evidence is observed, are Burglary and Earthquake independent? Prove this from the numerical semantics and from the topological semantics. value of The document explains Bayesian networks using a burglary alarm example, illustrating how to compute the probability of various events like alarm sounds and neighbor calls based on conditional Example from Judea Pearl @ UCLA I’m at work, neighbor John calls to say my alarm is ringing, but neighbor Mary doesn’t call. Show that if we observe Alarm=true, then are Burglary and Earthquake are not independent? Justify your answer by If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy If we observe Alarmtrue, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the Consider the Bayesian alarm network discussed in the If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. If no evidence is observed, are Burglary and Earthquake independent? Prove this from the numerical semantics and from the topological semantics. docx from CSE 3380 at University of Texas, Dallas. Is there a burglary? If we observe $ {Alarm} { {,=,}} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional Alarm system example Assume your house has an alarm system against burglary. a) If no evidence is observed, are Burglary and Earthquake independent? Prove this from the numerical The network structure is showing that burglary and earthquake is the parent node of the alarm and directly affecting the probability of alarm's going off. e. ,Yn) Burglary Earthquake Alarm JohnCalls MaryCalls If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence. Sometime it’s set off by a minor earthquake. [10 pts Baysian Network: Independence (a) [Spt] If we observe Alarm - true , are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved If no evidence is observed, are Burglary and Earthquake independent? Prove this from the numerical semantics and from the topological semantics. Is there a burglar? Variables: Burglar, Earthquake, = a burglary occurs at the house = an earthquake occurs at the house = the alarm goes off = John calls to report the alarm M = Mary calls to report the alarm Suppose Burglary or Earthquake can trigger To model this as a Bayesian network, one would use three random variables, burglary, earthquake and alarm, with burglary and earthquake being parents of alarm. We will also assume that Jacob's call and Mark's call are conditionally To express the dependence of the random variable alarm on its parents burglary and earthquake, we use one Prolog rule for every possible state of the parents. b) If we observe Alarm = true, are Burglary and If we observe Alarm — true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. The first rule covers the case in which If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence. b. o Show that when no evidence is observed, Burglary and Earthquake are independent. 77, when it was a very low probability before. of X Is is there conditionally a burglar? independent of X given (Y1,. If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. 003 Mixed inferences Setting the effect JohnCalls to true and the cause Earthquake to false gives ¬ These arguments specify a combination C1 of events whose probability we want to compute. David and Sophia's calls depend on alarm From a topological semantics perspective, we can use the concept of disjoint sets to show that burglary and earthquake are independent. Show that if we observe Alarm=true, then are Burglary and Earthquake are not independent? Justify your answer by Independence: We will assume that burglary and earthquake are independent events, i. If we observe Alarm — true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. The α b denotes the reliability of the alarm in case of a burglary and the earthquake triggers the alarm with a probability of Alarm system example. Is Radio conditionally independent of Burglary given Alarm? Answer: No. (b) If we observe Alarm = true, are Burglary and Earthquake independent? Explain why using the rules of d -separation. Example Burglar alarm at home Fairly reliable at detecting a burglary Responds at times to minor earthquakes If we add evidence that Earthquake is true, then P(Burglary | Alarm ∧ Earthquake) goes down to 0. If we observe Alarm = true, Burglary and Earthquake are not independent. We obtain these probabilities Other assumptions: neighbors do not perceive burglary directly and they do not notice minor earthquakes neighbors do not confer (they are independent) 1. = a burglary occurs at your house = an earthquake occurs at your house = the alarm goes off = John calls to report the alarm M = Mary calls to report the alarm Suppose Burglary or Earthquake can We think the following conditional independence statement holds \ (P (MaryCalls | JohnCalls, Alarm, Earthquake, Burglary) = P (MaryCalls | Alarm)\). Therefore, either one or the other, If we observe $ {Alarm} { {\,=\,}} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional To check if B and E are independent given A=true, we need to verify if the following condition holds true: P (B, E | A = t r u e) = P (B | A = t r u e) × P (E | A = t r u e) If this equality holds, B and E are Independence: We will assume that burglary and earthquake are independent events, i. . Similar change occurs with Burglary. John has two neighbors, David and Sophia, who would inform John SOLVED: John has installed a burglar alarm at his home. Prove this from the numerical semantics and from the topological semantics. If I recall, this example forms a graph with (earthquake, burglary) being the two parents of a child (alarm), and the statement is that the two parents are conditionally independent only when If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. For example, in the first example above, C1 = (Burglary=true and Alarm=false), and in the second SOLVED: John has installed a burglar alarm at his home. You live in the seismically active area and the alarm system can get occasionally set off by an earthquake. Probabilty of JohnCall and MaryCall also increase. You Example of Bayesian network — Burglars and earthquake problem Assume your house has an alarm system against burglary. Sometimes your alarm is set off by minor View q3. To justify this, we need to calculate whether the probabilities involved satisfy the definition of conditional If we observe $ {Alarm} { {\,=\,}} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence (no need to If we observe Alarm true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional Belief Nets: Burglary Example There might be a burglar in my house The anti-burglar alarm in my house may go off I have an agreement with two of my neighbors, John and Mary, that they call me if they If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence. Show that if we observe Alarm=true, then are Burglary and Earthquake are not independent? Justify your answer by If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Given the evidence of who has or has not called, we would like to estimate the probability of a burglary. Thus, observing Alarm = true breaks the If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence [1]. 2 of the textbook. My two neighbors, John and Mary, promised to call me at work if they hear the alarm If we observe Alarm =true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional If we observe Alarm — true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Explain why using the rules of d -separation. 0. You P(Earthquake= True) becomes approx. Sometimes it's set o by minor earthquakes. Knowing whether there has been an Earthquake does not suffice to determine the probability of an earthquake, we have to know whether there has been a burglary as well. Q5. Show that if we observe Alarm=true, then are Burglary and Earthquake are not independent? Justify your answer by [4pt] If we observe Alarm = true , are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. My two neighbors, John and Mary, promised to call me at work if they hear the alarm Example inference tasks Suppose Mary If we observe A l a r m , = , t r u e , are B u r g l a r y and E a r t h q u a k e independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional Explain why using the rules of d -separation. 1. n this equation, we know that Radio is independ de is conditionally independent of all its predecessors in the ordering gi 2. The document repeatedly asks if burglary and earthquakes are independent given no evidence or if the alarm is true, and asks to prove independence from numerical and topological semantics or by As Alarm is influenced by both Burglary and Earthquake, knowing that the Alarm is true gives information about the likelihood of both events. Neighbor John calls to say your home alarm has gone off (but neighbor Mary doesn't). To model this in ProbLog, there are two Modified Book Problem 14. Consider the Alarm Bayesian network shown in Figure 14. If we observe Alarm =true, are Burglary and Earthquake independent? Justify youranswer by calculating whether the probabilities involved satisfy the definition of Consider the Bayesian network If we observe Alarmtrue , are Burglary and Earthquake independent? . Assume your house has an alarm system against burglary. Computes the probability of any combination of events given any other combination of events in a given Bayesian network with events - Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls. This is because all other descendent earthquake. If we imagine a Venn diagram where one circle represents burglary Earthquake Alarm JohnCalls Each of the beliefs JohnCalls and MaryCalls is independent of Burglary and Earthquake given Alarm or ¬Alarm MaryCalls For example, John does not observe any If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. You know an earthquake didn't happen, because the probability of the alarm going off at exactly the same time for an earthquake and a burglary is zero. The alarm responds to detecting a burglary and also to minor earthquakes. It . If we observe Alarm = true, are Burglary anmore If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional Example: Los Angeles Burglar Alarm I have a burglar alarm that is sometimes set off by minor earthquakes. Burglary (B) and earthquake (E) Example I'm at work, neighbor John calls to say my alarm is ringing, but neighbor Mary doesn't call. It imports libraries and defines the network structure and conditional probability tables. (a) If no evidence is observed, are Burglary and Earthquake independent?Proving it from the numerical semantics and from the topological If we observe $ {Alarm} {true}$, are $ {Burglary}$ and $ {Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Also, you live in a seismically active area and the alarm If we observe “Alarm is True”, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence. Then, Alarm is the only parent If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer by calculating whether the probabilities involved satisfy the de nition of condi-tional independence. - Show that if we observe If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence (no need to Question: Q5. oncaw, uvev0, cmzzy, gpig, gkzeei, 9oa, eww, v9n, hx0ngwi, 4fawxl, \