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I am studying the book Bayesian Artificial Intelligence. There is an example bayesian network see the figure:

bayesian network

For this network the author calculated some numbers. I could not understand how author calculated highlighted probabilities for Xray and Dyspnoea when there is no evidence. See the figure please:

enter image description here

I am trying to reproduce the results represented in the table. If you can at least help me with no evidence column, I guess I can replicate reproduce remaining ones. However, I don't mind seeing the calculation for other reasoning cases (i.e. diagnostic or predictive or intercausal). Bel refers to posterior probability. E.g., Bel(D=T) refers to posterior probability of Dyspnoea being true.

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It is a simple calculation using law of total probability: $$P(X=pos) = P(X=pos|C=T)P(C=T)+P(X=pos|C=F)P(C=F) = 0.9\,P(C=T) + 0.2\, P(C=F) = 0.9\cdot 0.011 + 0.2\cdot (1-0.011) = 0.2077 \approx 0.208 $$ The other things P(D=T) etc are computed in the same way.

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  • $\begingroup$ Thanks for the answer. For predictive reasoning, this works great. Can you also provide how diagnostic and intercausal numbers are calculated. One example for calculation is enough for each reasoning. Thanks again $\endgroup$ – alan turing Jan 10 '17 at 6:30
  • $\begingroup$ You need to use Bayes theorem and the network. I.e. for P(S=T|D=T) (2nd row diagnostic) $ P(S=T|D=T) = P(D=T|S=T)P(S=T)/P(D=T) $ (Bayes theorem) $P(D=T|S=T)=P(D=T|C=T)P(C=T|S=T)+P(D=T|C=F)P(C=F|S=T)$ $\endgroup$ – sega_sai Jan 10 '17 at 18:14

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