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enter image description hereI have a Question about Bayesian Networks.

I have a network with many parent nodes and one child node. I have the probabilities for the parents and for the child. The child node is binary, so there are just two possible values for this node (true/false).

Now I want to calculate the probability that the child node is true. The values of the parents are all known. So I need to know how to calculate the probability for a true in the child node given all the values of the nodes in the parent generation.

1)How can I calculate this? (Do I have to calculate or can I implement it in something like a look-up table?)

2) If the values in every node of the parent generation would be uniformly distributed. Would I need the probabilities of the parent generation or could I just use the ones in the child generation?

Thanks

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As you have described it, there is not enough information to know how to conditional probability of the child from the parents. You have described that you have the marginal probabilities of each node; this tells you nothing about the relationship between nodes. For example, if you observed that 50% of people in a study take a drug (and the others take placebo), and then you later note that 20% of the people in the study had an adverse outcome, you do not have enough information to know how the probability of the child (adverse outcome) depends on the probability of the parent (taking the drug). You need to know the joint distribution of the parents and child to learn the conditional distribution. The joint distribution requires that you know the probability of the combination of all possible values for the parents and the children. From the joint distribution, you can use the definition of conditional probability to find the conditional distribution of the child on the parents.

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  • $\begingroup$ What I mean meant with that I have the probability for the nodes is that I have the probability tables (CPD's or CPT's). I created the tables by parameter learning with the bnt toolbox for Matlab. (cs.ubc.ca/~murphyk/Software/BNT/…) So I think in the tables for the child node are the conditional probabilities. $\endgroup$ – user212361 Jun 21 '18 at 17:29

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