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Belief network problem

  1. Nov 16, 2007 #1
    I am having problem solving this exercise. The problem actually comes with a diagram but I do not know and I do not think i can draw it in the forum. The exercise is based on car starting(Heckerman 1995)

    Since I can't draw the network diagram here but values of probability are given but first let me define all the variables

    B - Battery
    G - Gauge
    F - Fuel
    T - Turnover
    S - Start
    N - No
    Y - Yes

    P(B = N) = 0.02
    p(F = N) = 0.05
    P(G = N|B = Y, F = Y) = 0.04
    P(G = N|B = Y, F = N) = 0.97
    P(G = N|B = N, F = Y) = 0.10
    P(G = N|B = N, F = N) = 0.99
    P(T = N|B = Y) = 0.03
    P(T = N|B = N) = 0.98
    P(S = N|T = Y, F = Y) = 0.01
    P(S = N|T = Y, F = N) = 0.92
    P(S = N|T = N, F = Y) = 1.0
    P(S = N|T = N, F = N) = 1.0

    It was asked to calculate p(F = N|S = N)

    Im thinking of Bayesian but I got stuck somewhere so I think it is the wrong approach since S depend on F and T NOT F alone.

    Im thinking of the other approach and came up with an expression

    P(F = N|S = N) = P(S = N|F = N)/P(F)
    = P(S = N, B, G, T|F = N)/P(F)

    But I am not sure how to compute and put the figures together.

    Any input/help is appreciated. Thank you
     
  2. jcsd
  3. Nov 16, 2007 #2

    EnumaElish

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    How do you get P(F = N|S = N) = P(S = N|F = N)/P(F) ?

    P(F = N|S = N) = P(S = N & F = N)/P(S = N) and P(S = N|F = N) = P(S = N & F = N)/P(F = N) so P(S = N & F = N) = P(F = N|S = N)P(S = N) = P(S = N|F = N)P(F = N).
     
  4. Nov 16, 2007 #3
    So the Bayesian approach was right. I taught I was wrong at the first place because using Bayesian ended up with the following

    P(S = N|F = N) P(F = N)/ P(S = N)

    but from the diagram I have and as you can see from the probabilities, S depend on both F and T and in the expression above we want to know the probability of S = N given that F = N (in other words the probability that the engine will not start given that the fuel tank was empty).
     
  5. Nov 17, 2007 #4
    I am still having trouble solving P(S = N|F = N).

    plz help....
     
  6. Nov 19, 2007 #5

    EnumaElish

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    Below, I assume that the notation (A|B,C) means (A|B)|C = A|(B|C), and neither A|(B & C) nor (A|B) & C. (If anyone disagrees, please post your opinion.)

    P(S = N|F = N) = P(S = N|T = Y, F = N) P(T = Y) + P(S = N|T = N, F = N) P(T = N) so you should first derive P(T = Y) and P(T = N).

    You can derive P(T=N) from:
    P(B = N) = 0.02
    P(T = N|B = Y) = 0.03
    P(T = N|B = N) = 0.98
    using a formula similar to the one in the previous paragraph of this post.

    Then, P(T=Y) = 1 - P(T=N).
     
    Last edited: Nov 19, 2007
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