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Can anyone show me how to do this problem? Question 4: Sampling and Bayesian Network (25 points) We want to study people's exercise habits on sunny and rainy days. Suppose we consider the weather, along with a person's exercise, over the span of two days. We'll have four random variables: W and W stand for the weather on days 1 and 2, which can either be rainy (R) or sunny (S), and the variables E and E represent whether the person exercises on days 1 and 2 or not and take values T (for truly doing exercise) or F. We can model this as the following Dynamic Bayes Net with these probabilities. Note that this is a simple case of DBN and you can consider it as an HMM. W: P(W=S) = 0.6, P(W=R) = 0.4 W': P(W'=S|W=S) = 0.7, P(W'=R|W=S) = 0.3, P(W'=S|W=R) = 0.5, P(W'=R|W=R) = 0.5 W S E P(E|W=T) = 0.9, P(E|W=F) = 0.1, P(E|W=T') = 0.2, P(E|W=F') = 0.8 S R R Suppose we produce the following sample of (W,E,W',E') from the exercise model: R,F,R,T S,T,S,T S,T,S,T S,T,R,F R,F,S,T R,F,R,F S,F,S,T S,T,S,T S,T,R,F a) What is P(W=R), the probability that sampling assigns to the event W=R? b) Assume we're computing P(W=B=T,E=F). Cross off samples above which are rejected by rejection sampling. Rejection sampling seems to be wasting a lot of effort, so we decide to switch to likelihood weighting. Assume we generate the following six samples given the evidence and E=F: W,E,W',E' = S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F c) What is the weight of the first sample (S,T,R,F) above? d) Using likelihood weighting, estimate P(W=E=T,E=F). 

          Can anyone show me how to do this problem?
Question 4: Sampling and Bayesian Network (25 points) We want to study people's exercise habits on sunny and rainy days. Suppose we consider the weather, along with a person's exercise, over the span of two days. We'll have four random variables: W and W stand for the weather on days 1 and 2, which can either be rainy (R) or sunny (S), and the variables E and E represent whether the person exercises on days 1 and 2 or not and take values T (for truly doing exercise) or F. We can model this as the following Dynamic Bayes Net with these probabilities. Note that this is a simple case of DBN and you can consider it as an HMM.

W: P(W=S) = 0.6, P(W=R) = 0.4
W': P(W'=S|W=S) = 0.7, P(W'=R|W=S) = 0.3, P(W'=S|W=R) = 0.5, P(W'=R|W=R) = 0.5
W S
E
P(E|W=T) = 0.9, P(E|W=F) = 0.1, P(E|W=T') = 0.2, P(E|W=F') = 0.8
S
R R

Suppose we produce the following sample of (W,E,W',E') from the exercise model: R,F,R,T S,T,S,T S,T,S,T S,T,R,F R,F,S,T R,F,R,F S,F,S,T S,T,S,T S,T,R,F

a) What is P(W=R), the probability that sampling assigns to the event W=R?
b) Assume we're computing P(W=B=T,E=F). Cross off samples above which are rejected by rejection sampling. Rejection sampling seems to be wasting a lot of effort, so we decide to switch to likelihood weighting. Assume we generate the following six samples given the evidence and E=F: W,E,W',E' = S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F
c) What is the weight of the first sample (S,T,R,F) above?
d) Using likelihood weighting, estimate P(W=E=T,E=F).
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can anyone show me how to do this problem questlon 4saupling and bayesian network25 points we want to study pcoples cxercise habit on sunny and rainy days suppose we consider the weather alo 59743

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Can anyone show me how to do this problem? Question 4: Sampling and Bayesian Network (25 points) We want to study people's exercise habits on sunny and rainy days. Suppose we consider the weather, along with a person's exercise, over the span of two days. We'll have four random variables: W and W stand for the weather on days 1 and 2, which can either be rainy (R) or sunny (S), and the variables E and E represent whether the person exercises on days 1 and 2 or not and take values T (for truly doing exercise) or F. We can model this as the following Dynamic Bayes Net with these probabilities. Note that this is a simple case of DBN and you can consider it as an HMM. W: P(W=S) = 0.6, P(W=R) = 0.4 W': P(W'=S|W=S) = 0.7, P(W'=R|W=S) = 0.3, P(W'=S|W=R) = 0.5, P(W'=R|W=R) = 0.5 W S E P(E|W=T) = 0.9, P(E|W=F) = 0.1, P(E|W=T') = 0.2, P(E|W=F') = 0.8 S R R Suppose we produce the following sample of (W,E,W',E') from the exercise model: R,F,R,T S,T,S,T S,T,S,T S,T,R,F R,F,S,T R,F,R,F S,F,S,T S,T,S,T S,T,R,F a) What is P(W=R), the probability that sampling assigns to the event W=R? b) Assume we're computing P(W=B=T,E=F). Cross off samples above which are rejected by rejection sampling. Rejection sampling seems to be wasting a lot of effort, so we decide to switch to likelihood weighting. Assume we generate the following six samples given the evidence and E=F: W,E,W',E' = S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F S,T,R,F c) What is the weight of the first sample (S,T,R,F) above? d) Using likelihood weighting, estimate P(W=E=T,E=F).
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Transcript

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0:00 Hello everyone.
00:02 So as for the given information about the weather, it is given that we can predict the weather using a simple markup model consists of three states.
00:14 The three states are sunny, rainy, snowy.
00:28 Right? so here we'll write sunny, rainy, snowy.
00:39 Okay.
00:40 So it is given that every sunny day is followed by another sunny day.
00:46 With the probability of 0 .8.
00:48 So this becomes 0 .8.
00:51 Next, the probability of rainy day after a sunny day is 0 .15.
00:57 Okay, this is sunny day after this, rainy day is 0 .15.
01:03 Next it is given the probability of the rainy day following another rainy day...
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