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artificial-intelligenceprobabilitybayesianbayesian-networksprobability-theory

How to create a joint probability table from existing conditioinal probability tables? (CPTs)

I have the following tables ,with the dependencies below :

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And I want to create the joint-probability table for P(M,P,W,B) , which looks like this (and of course ,you can assume that the below table is not given to me , it is taken from the answer for this question) :

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Can someone please explain how can I create the joint probability table for P(M,P,W,B) ?

Much appreciate

Solution

  • The joint probability for P(M,P,W,B) is simply the product of the entries of the other tables. This is from Wikipedia:

    X is a Bayesian network with respect to G if its joint probability density function (with respect to a product measure) can be written as a product of the individual density functions, conditional on their parent variables:

    p (x) = \prod_{v \in V} p \big(x_v \,\big|\, x_{\operatorname{pa}(v)} \big)

    where pa(v) is the set of parents of v (i.e. those vertices pointing directly to v via a single edge).