Mixing
Understanding how to read Bayesian networks
$begingroup$
Below is an example that I want to talk about:
I'm going to define variable names based on the first letter as described in the bubbles. One question I have is how would I calculate $P(M|B)$? This is what I got so far: $$P(M|B) = dfrac{P(M,B)}{P(B)}$$
Since $P(B)$ is known then I move on to the numerator:
$$P(M,B) = P(M,B,J,E,A)+P(M,B,neg J, E,A)+P(M,B,J,neg E,A)+P(M,B,J, E,neg A)+P(M,B,neg J,neg E,A)+P(M,B,neg J, E,neg A)+P(M,B,J, neg E,neg A)+P(M,B,neg J, neg E,neg A)$$
Is this really the way? I'm surprised to see how much computation I have to do for such a small problem. Am I doing this correctly?
bayesian bayesian-network
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
$endgroup$
add a comment |
$begingroup$
Below is an example that I want to talk about:
I'm going to define variable names based on the first letter as described in the bubbles. One question I have is how would I calculate $P(M|B)$? This is what I got so far: $$P(M|B) = dfrac{P(M,B)}{P(B)}$$
Since $P(B)$ is known then I move on to the numerator:
$$P(M,B) = P(M,B,J,E,A)+P(M,B,neg J, E,A)+P(M,B,J,neg E,A)+P(M,B,J, E,neg A)+P(M,B,neg J,neg E,A)+P(M,B,neg J, E,neg A)+P(M,B,J, neg E,neg A)+P(M,B,neg J, neg E,neg A)$$
Is this really the way? I'm surprised to see how much computation I have to do for such a small problem. Am I doing this correctly?
bayesian bayesian-network
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
$endgroup$
add a comment |
$begingroup$
Below is an example that I want to talk about:
I'm going to define variable names based on the first letter as described in the bubbles. One question I have is how would I calculate $P(M|B)$? This is what I got so far: $$P(M|B) = dfrac{P(M,B)}{P(B)}$$
Since $P(B)$ is known then I move on to the numerator:
$$P(M,B) = P(M,B,J,E,A)+P(M,B,neg J, E,A)+P(M,B,J,neg E,A)+P(M,B,J, E,neg A)+P(M,B,neg J,neg E,A)+P(M,B,neg J, E,neg A)+P(M,B,J, neg E,neg A)+P(M,B,neg J, neg E,neg A)$$
Is this really the way? I'm surprised to see how much computation I have to do for such a small problem. Am I doing this correctly?
bayesian bayesian-network
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
$endgroup$
Below is an example that I want to talk about:
I'm going to define variable names based on the first letter as described in the bubbles. One question I have is how would I calculate $P(M|B)$? This is what I got so far: $$P(M|B) = dfrac{P(M,B)}{P(B)}$$
Since $P(B)$ is known then I move on to the numerator:
$$P(M,B) = P(M,B,J,E,A)+P(M,B,neg J, E,A)+P(M,B,J,neg E,A)+P(M,B,J, E,neg A)+P(M,B,neg J,neg E,A)+P(M,B,neg J, E,neg A)+P(M,B,J, neg E,neg A)+P(M,B,neg J, neg E,neg A)$$
Is this really the way? I'm surprised to see how much computation I have to do for such a small problem. Am I doing this correctly?
bayesian bayesian-network
bayesian bayesian-network
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
asked Jan 24 at 5:37
Ayumu KasuganoAyumu Kasugano
20517
20517
add a comment |
add a comment |
1 Answer
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$begingroup$
Well, the joint probability distribution is
$$p(B,E,A,J,M) = p(B) p(E) p(Amid B,E) p(Jmid A) p(Mmid A).$$
What your are looking for is the marginal distribution
$$p(M,B) = sum_{E,A,J} p(B,E,A,J,M),$$
where the sum is over all values of $E,A,J$ and this is what you did right!
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Well, the joint probability distribution is
$$p(B,E,A,J,M) = p(B) p(E) p(Amid B,E) p(Jmid A) p(Mmid A).$$
What your are looking for is the marginal distribution
$$p(M,B) = sum_{E,A,J} p(B,E,A,J,M),$$
where the sum is over all values of $E,A,J$ and this is what you did right!
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
$endgroup$
add a comment |
$begingroup$
Well, the joint probability distribution is
$$p(B,E,A,J,M) = p(B) p(E) p(Amid B,E) p(Jmid A) p(Mmid A).$$
What your are looking for is the marginal distribution
$$p(M,B) = sum_{E,A,J} p(B,E,A,J,M),$$
where the sum is over all values of $E,A,J$ and this is what you did right!
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
$endgroup$
add a comment |
$begingroup$
Well, the joint probability distribution is
$$p(B,E,A,J,M) = p(B) p(E) p(Amid B,E) p(Jmid A) p(Mmid A).$$
What your are looking for is the marginal distribution
$$p(M,B) = sum_{E,A,J} p(B,E,A,J,M),$$
where the sum is over all values of $E,A,J$ and this is what you did right!
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
$endgroup$
Well, the joint probability distribution is
$$p(B,E,A,J,M) = p(B) p(E) p(Amid B,E) p(Jmid A) p(Mmid A).$$
What your are looking for is the marginal distribution
$$p(M,B) = sum_{E,A,J} p(B,E,A,J,M),$$
where the sum is over all values of $E,A,J$ and this is what you did right!
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
answered Jan 24 at 8:39
WuestenfuxWuestenfux
5,1271513
5,1271513
add a comment |
add a comment |
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