Consider the Bayesian Network below whose variables are Boolean and can take on values T and...

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Consider the Bayesian Network below whose variables are Boolean and can take on values T and F: P(B) P(E) Burglary Earthquake .001 .002 BTTFF BE P(AIB,E) TT TFTF .95 Alarm F .94 .29 .001 A P(JIA) A P(MIA) JohnCalls T.90 MaryCalls T .70 F .05 F .01 ⚫ Write down an expression for p(B, E, A, J, M) using the conditional inde- pendencies implied by the structure of the Bayes net. ⚫ Compute the value of that expression as a number. Show your work. ⚫ Compute the value of p(E, J, M) by hand. Show all of your work. That requires computing and summing 4 joint probability values using the Bayes net above. If the value of p(J, M) = 0.002084100239, what is the value of p(E|J, M)? Write a function to sample values from the joint distribution defined by this network. Use that function to sample instances and use those sam- ples to estimate p(E, J, M) and p(J, M). Use those estimates to estimate p(E|J, M). Turn in your code and show the counts that you used to estimate the probabilities and the probabilities themselves. How many samples do you need to draw to get a good estimate of p(E|J, M)? Why does it take such a large number of samples? (For what it's worth, I wrote a 28 line python solution to this question.) Consider the Bayesian Network below whose variables are Boolean and can take on values T and F: P(B) P(E) Burglary Earthquake .001 .002 BTTFF BE P(AIB,E) TT TFTF .95 Alarm F .94 .29 .001 A P(JIA) A P(MIA) JohnCalls T.90 MaryCalls T .70 F .05 F .01 ⚫ Write down an expression for p(B, E, A, J, M) using the conditional inde- pendencies implied by the structure of the Bayes net. ⚫ Compute the value of that expression as a number. Show your work. ⚫ Compute the value of p(E, J, M) by hand. Show all of your work. That requires computing and summing 4 joint probability values using the Bayes net above. If the value of p(J, M) = 0.002084100239, what is the value of p(E|J, M)? Write a function to sample values from the joint distribution defined by this network. Use that function to sample instances and use those sam- ples to estimate p(E, J, M) and p(J, M). Use those estimates to estimate p(E|J, M). Turn in your code and show the counts that you used to estimate the probabilities and the probabilities themselves. How many samples do you need to draw to get a good estimate of p(E|J, M)? Why does it take such a large number of samples? (For what it's worth, I wrote a 28 line python solution to this question.)

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Using the conditional independencies inferred by the Bayesian networks topology write an equation for pBEAJM Determine the numerical value of the equa... View the full answer