Consider the Burglary network discussed, with the nodes B(urglary), E(arthquake)

Question

Consider the Burglary network discussed, with the nodes B(urglary), E(arthquake), A(larm), J(ohn calls), and M(ary calls).

Using enumeration, compute the probability P(b | j,NOT m), i.e., of a burglary having occurred, given that John has called and Mary has not called.

Using variable elimination, compute the probability P(b,NOT e | j,m).

Considering the same network, note that each of the 5 variables in the network is boolean, i.e., can take two possible values. Hence, in order to determine the marginal distributions of each variable, it is sufficient to determine the probability of one of the possible outcomes for each variable. Using the sum-product algorithm, compute the marginal probabilities P(b), P(e), P(a), P(j), P(m).

Chapter 14. robabil 14.2. Section Earthquake POE) POB) Burglary 512 002 B E POA) t t 95 Alarm 94 t 29 f f .001 14.2 TH A P(J) Mary Calls JohnCalls t 90 t .70 f .05 f .01 Figure 14.2 A typical Bayesian network, showing both the topology and the co Earthquake, Alarm, JohnCalls, and MaryCalls, respectively. the alarm and calls then, too M on the other hand, likes rather loud musk misses the alarm altogether. Given the evidence of who has or as not cal we to estimate the probability of a burglary A Bayesian network for thi shows that

Explanation / Answer

Probabilities is also either marginal, joint or conditional. Understanding their variations and the way to govern among them is essential to success in understanding the foundations of statistics.

Marginal chance: the probability of an incident occurring (p(A)), it should be thought of as associate unconditional chance. it's not conditioned on another event. Example: the chance that a card drawn is red (p(red) = zero.5). Another example: the chance that a card drawn could be a four (p(four)=1/13).

Joint probability: p(A and B). The chance of event A and event B occurring. it's the chance of the intersection of 2 or a lot of events. The chance of the intersection of A and B is also written p(A B). Example: the chance that a card could be a four and red =p(four and red) = 2/52=1/26. (There area unit 2 red fours during a deck of fifty two, the four of hearts and also the four of diamonds).

Conditional chance: p(A|B) is that the probability of event A occurring, provided that event B happens. Example: provided that you thespian a red card, what’s the chance that it’s a four (p(four|red))=2/26=1/13. thus out of the twenty six red cards (given a red card), there area unit 2 fours thus 2/26=1/13.

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