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pythonpymc3pymcbayesian-networksexpectation-maximization
danitalpi
danitalpi

Reputation: 1

Compute probability of parameters given data in a bayesian network with pyMC3

I’m new to pyMC3 and I would like to know if it is possible to use it to solve the following problem: I have a bayesian network (image of my BN: Bayesian network of my problem) and I don’t know the parameters of the distributions of A,B,C,D and S, I just know the type of distribution (there are both discrete and continuous distributions). I have data from A,B,C and D (thus S is a hidden variable and it is discrete) and my goal is to determine the probability of S given the observed data. I know that one approach is to use the expectation maximization algorithm but I was wondering if it is possible to solve the problem with pyMC3. Thank you. Best regards, Daniele.

Upvotes: 0

Views: 262

Answers (1)

sam
sam

Reputation: 2311

I believe you can solve the problem only when you know how S is related to A, B, C and D.

If as mentioned in the image, S is impacted by all of them equally, you can write

S = A + B

If we know S is a binary then we can write,

S =  1/ (1 + exp(A+ B))

Then you can define A, B, C, and D in terms of their distributions. pyMC3 will run an MCMC simulation to estimate the parameters of the distribution. With the mean of those parameters, you can estimate A, B, C, and D which after addition will give you S.

Upvotes: 0

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