Is this Bayesian Network Probability calculation correct?
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I think I understand how to calculate BN and why it is so, but complex net still confuses me. Currently how I understand it is that, if there is any 'result' variable in the probability, it can be calculated by converting it to P(result|cause)P(cause). So I assumed in this bayesian network (A,B → C → D,E), if you want to get P(B,E), every parent and grand parent of B and E should be considered. As B doesn't have parent, only the (grand) parent of E (A,C) will hop in, and finally it can be calculated as :
P(B,E)
= P(B,E,A,C)+P(B,E,~A,C)+P(B,E,A,~C)+P(B,E,~A,~C)
The joint probability would be :
P(B,E,A,C) = P(B)P(A)P(C|A,B)P(E|C)
The rest of them are calculated the same way. I'd like to check if this calculation and my understanding is right. Thank you!
probability bayesian conditional-probability bayesian-network
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
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add a comment |
$begingroup$
I think I understand how to calculate BN and why it is so, but complex net still confuses me. Currently how I understand it is that, if there is any 'result' variable in the probability, it can be calculated by converting it to P(result|cause)P(cause). So I assumed in this bayesian network (A,B → C → D,E), if you want to get P(B,E), every parent and grand parent of B and E should be considered. As B doesn't have parent, only the (grand) parent of E (A,C) will hop in, and finally it can be calculated as :
P(B,E)
= P(B,E,A,C)+P(B,E,~A,C)+P(B,E,A,~C)+P(B,E,~A,~C)
The joint probability would be :
P(B,E,A,C) = P(B)P(A)P(C|A,B)P(E|C)
The rest of them are calculated the same way. I'd like to check if this calculation and my understanding is right. Thank you!
probability bayesian conditional-probability bayesian-network
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
$endgroup$
add a comment |
$begingroup$
I think I understand how to calculate BN and why it is so, but complex net still confuses me. Currently how I understand it is that, if there is any 'result' variable in the probability, it can be calculated by converting it to P(result|cause)P(cause). So I assumed in this bayesian network (A,B → C → D,E), if you want to get P(B,E), every parent and grand parent of B and E should be considered. As B doesn't have parent, only the (grand) parent of E (A,C) will hop in, and finally it can be calculated as :
P(B,E)
= P(B,E,A,C)+P(B,E,~A,C)+P(B,E,A,~C)+P(B,E,~A,~C)
The joint probability would be :
P(B,E,A,C) = P(B)P(A)P(C|A,B)P(E|C)
The rest of them are calculated the same way. I'd like to check if this calculation and my understanding is right. Thank you!
probability bayesian conditional-probability bayesian-network
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
$endgroup$
I think I understand how to calculate BN and why it is so, but complex net still confuses me. Currently how I understand it is that, if there is any 'result' variable in the probability, it can be calculated by converting it to P(result|cause)P(cause). So I assumed in this bayesian network (A,B → C → D,E), if you want to get P(B,E), every parent and grand parent of B and E should be considered. As B doesn't have parent, only the (grand) parent of E (A,C) will hop in, and finally it can be calculated as :
P(B,E)
= P(B,E,A,C)+P(B,E,~A,C)+P(B,E,A,~C)+P(B,E,~A,~C)
The joint probability would be :
P(B,E,A,C) = P(B)P(A)P(C|A,B)P(E|C)
The rest of them are calculated the same way. I'd like to check if this calculation and my understanding is right. Thank you!
probability bayesian conditional-probability bayesian-network
probability bayesian conditional-probability bayesian-network
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
asked Dec 12 '18 at 16:26
PuffedRiceCrackersPuffedRiceCrackers
83
83
add a comment |
add a comment |
1 Answer
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For the DAG: $$begin{array}{ccc}A&&&&B\&searrow&&swarrow \&&C\&swarrow&&searrow\D&&&&Eend{array}$$
Then, yes,$$P_{B,E}=sum_{A,C}P_AP_BP_{Cmid A, B}P_{Emid C}$$
$endgroup$
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1 Answer
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1 Answer
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$begingroup$
For the DAG: $$begin{array}{ccc}A&&&&B\&searrow&&swarrow \&&C\&swarrow&&searrow\D&&&&Eend{array}$$
Then, yes,$$P_{B,E}=sum_{A,C}P_AP_BP_{Cmid A, B}P_{Emid C}$$
$endgroup$
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For the DAG: $$begin{array}{ccc}A&&&&B\&searrow&&swarrow \&&C\&swarrow&&searrow\D&&&&Eend{array}$$
Then, yes,$$P_{B,E}=sum_{A,C}P_AP_BP_{Cmid A, B}P_{Emid C}$$
$endgroup$
add a comment |
$begingroup$
For the DAG: $$begin{array}{ccc}A&&&&B\&searrow&&swarrow \&&C\&swarrow&&searrow\D&&&&Eend{array}$$
Then, yes,$$P_{B,E}=sum_{A,C}P_AP_BP_{Cmid A, B}P_{Emid C}$$
$endgroup$
For the DAG: $$begin{array}{ccc}A&&&&B\&searrow&&swarrow \&&C\&swarrow&&searrow\D&&&&Eend{array}$$
Then, yes,$$P_{B,E}=sum_{A,C}P_AP_BP_{Cmid A, B}P_{Emid C}$$
answered 2 days ago
community wiki
Graham Kemp
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