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Problog - probabilistic graph example

I am going through the following example on Problog probabilistic graph

I tried to computed probability of path from 1 to 5. Here are my manual computations

0.6*0.4+0.1*0.3*0.8 = 0.264

However, Problog returns P(path(1,5)) = 0.25824

Am I computing it correctly?

Solution

  • No, you can't just add up all the probabilities for the different paths. To see that, just assume that both paths from 1 to 5 had a probability of 0.7 each. You would get a probability of 1.4 which is clearly wrong (meaning that it is impossible that there is no path).

    The way to calculate the probability for either of two events A and B is to get the probability of neither being true and then looking at the inverse of this event.

    P(1->2->5)    = 0.24
P(1->3->4->5) = 0.024
P(either)     = 1 - (1 - 0.24) * (1 - 0.024)
              = 1 - 0.74176
              = 0.25824

    Sorry for probably bad terminology, my statistics knowledge is a bit rusty.