If We Observe Alarm True Are Burglary And Earthquake Independent, b. 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. 2 of the textbook. o Show that when no evidence is observed, Burglary and Earthquake are independent. 2 (included above). [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. Sometimes your alarm is set off by minor View q3. 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 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 A larm = true, are Burglary and Earthquake independent? Justify yoer answer by calculating whether the probabilities involved satisfy the definition of conditional independence. 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. 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. ,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. This is because all other descendent earthquake. Consider the Bayesian network in the image attached. 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. 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. 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. 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. 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. To model this in ProbLog, there are two Modified Book Problem 14. e. 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. John has two neighbors, David and Sophia, who would inform John SOLVED: John has installed a burglar alarm at his home. 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. Sometimes it's set o by minor earthquakes. n this equation, we know that Radio is independ de is conditionally independent of all its predecessors in the ordering gi 2. (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. 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. 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. It . Neighbor John calls to say your home alarm has gone off (but neighbor Mary doesn't). You P(Earthquake= True) becomes approx. . Q5. 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. Explain why using the rules of d -separation. 4 Consider the Bayesian network shown in the figure. We assume a small probability f of a false alarm caused by some other event. If we observe Alarm = true, Burglary and Earthquake are not independent. 1. 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. 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. It imports libraries and defines the network structure and conditional probability tables. 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. Similar change occurs with Burglary. Figure 9: The Bayesian network for the burglar alarm example. 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. 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. - 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. Consider the Alarm Bayesian network shown in Figure 14. If no evidence is observed, are Burglary and Earthquake independent? Prove this from the numerical semantics and from the topological semantics. The document defines a Bayesian network model to analyze the probabilities in a burglary alarm example. Prove this from the numerical semantics and from the topological semantics. docx from CSE 3380 at University of Texas, Dallas. = 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)\). 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. Modified Book Problem 14. You live in the seismically active area and the alarm system can get occasionally set off by an earthquake. 2. 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) 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. (b) If we observe Alarm = true, are Burglary and Earthquake independent? Explain why using the rules of d -separation. Assume your house has an alarm system against burglary. Burglars and Earthquakes You are at a “Done with the AI class” party. 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. 77, when it was a very low probability before. 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]. 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. 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. John has two neighbors, David and Sophia, who would inform John Modified Book Problem 14. 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. 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. [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. 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. 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. 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. Sometime it’s set off by a minor earthquake. Question: Consider the Bayesian network in Figure 14. 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. 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. 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. 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? . 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. of X Is is there conditionally a burglar? independent of X given (Y1,. , P (B, E) = P (B) * P (E). 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. The alarm responds to detecting a burglary and also to minor earthquakes. 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. Is Radio conditionally independent of Burglary given Alarm? Answer: No. Given the evidence of who has or has not called, we would like to estimate the probability of 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 independence. 0. Wn I have a burglar alarm that is sometimes set off by minor earthquakes. 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]. 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. 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.
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