Assume the Bayes net, and the corresponding distributions over the variables in the Bayes net from Figure S13.46. 

a. Your task is now to estimate P(+y | + x, +z) using rejection sampling. Below are some samples that have been produced by prior sampling (that is, the rejection stage in rejection sampling hasn’t happened yet). Which of the following samples would be rejected by rejection sampling?

(i) +x, +y, +z 

(ii) −x, +y, +z 

(iii) −x, −y, +z (iv) +x, −y, −z (v) +x, −y, +z 

b. Using rejection sampling, give an estimate of P(+y | + x, +z) from the five prior samples, or state why it cannot be computed.

c. Using the following samples (which were generated using likelihood weighting), estimate

P(+y | + x, +z) using likelihood weighting, or state why it cannot be computed. 

(i) +x, +y, +z 

(ii) +x, −y, +z 

(iii) +x, +y, +z 

d. Given a sequence of samples, each specifying a value for all the variables in the network, how can one tell if the sequence could have been generated by Gibbs sampling?

Figure S13.46

Transcribed Image Text:

X P(X) +x2/5 3/5 -I X Y +y +x -y +x XP(YX) 2/3 1/3 3/4 1/4 Y +y-x -y-x Z ZY P(Z Y) +z+y - z+y +z-y -z-y 1/3 2/3 1/5 4/5