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"""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