Bayesian nets in RDF, and how to update them

I've banged my head on this for a couple of days and feel close to a solution. The graph looks like this.



Each random boolean variable gets a node, the causal relationship between them gets a node, and each variable gets a probability.
The math for updating probabilities is a little tricky, but in a fun and interesting way, so I enjoyed banging on that. At some point I'll tackle more involved cases where there aren't simply two random boolean variables, but that's the logistically simple case that exposes most of the concepts involved. Kinda like the Drosophila of Bayesian inference.

"""Let A and B be random boolean variables, with A being an

unobservable cause and B being an observable effect, and Pr(B|A) and

Pr(B|~A) are given. This might be the case if the situation has some

structure that dictates the conditional probabilities, like a 6.432

problem, or it just might be empirical.

From these we can compute probabilities for the four cases.

P11 = Pr(B^A) = Pr(A) Pr(B|A)

P10 = Pr(~B^A) = Pr(A) (1-Pr(B|A))

P01 = Pr(B^~A) = (1-Pr(A)) Pr(B|~A)

P00 = Pr(~B^~A) = (1-Pr(A)) (1-Pr(B|~A))

Treat (Pr(B|A), Pr(B|~A)) as one piece of information, and Pr(A) as a

separate independent piece of information. The first piece reflects

your beliefs about the machinery connecting A to B, and the second

reflects your beliefs about the likelihood of A, so these are

legitimately separate concerns.

If we observe that B=1, then we want to replace Pr(A) with our

previous estimate for Pr(A|B), which is given by our old numbers as

P11/Pr(A) = P11/(P11+P01), and this becomes our posterior probability

for A."""

class Link1:

def __init__(self, PrBgivenA, PrBgivenNotA):

self.PrBgivenA, self.PrBgivenNotA = PrBgivenA, PrBgivenNotA

def updatePrA(self, PrA, bvalue):

p11 = PrA * self.PrBgivenA

p10 = PrA * (1. - self.PrBgivenA)

p01 = (1. - PrA) * self.PrBgivenNotA

p00 = (1. - PrA) * (1. - self.PrBgivenNotA)

# print p11, p01, p10, p00

assert 0.999 < p11 + p01 + p10 + p00 < 1.001

assert PrA - 0.001 < p10 + p11 < PrA + 0.001

if bvalue:

# Pr(A|B)

newPrA = p11 / (p11 + p01)

else:

# Pr(A|~B)

newPrA = p10 / (p10 + p00)

assert 0.0 <= newPrA <= 1.0

return newPrA

link = Link1(0.6, 0.27)

PrA = 0.5

print PrA

for i in range(5):

PrA = link.updatePrA(PrA, 0)

print PrA

for i in range(10):

PrA = link.updatePrA(PrA, 1)

print PrA