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Of Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA, pp. 102–110. 36 Bayesian Network Bozdogan, H. (1987). Model selection and akaike’s information criteria (AIC): The general theory and its analytical extentions, Psychometrika 52: 354–370. Charniak, E. (1991). Bayesian networks without tears, AI Magazine 12(4): 50–63. , Bell, D. A. & Liu, W. (2002). Learning belief networks from data: An information theory based approach, Artificial Intelligence 1-2: 43–90. Chickering, D.
For example, the probability that the sprinkler was on, given that the pavement is slippery, is P( X3 = on| X5 = true) P( X3 = on, X5 = true) = P( X5 = true) ∑ x1 ,x2 ,x4 P( x1 , x2 , X3 = on, x4 , X5 = true) = ∑ x1 ,x2 ,x3 ,x4 P( x1 , x2 , x3 , x4 , X5 = true) = (4) ∑ x1 ,x2 ,x4 P( x1 ) P( x2 | x1 ) P( X3 = on| x1 ) P( x4 | x2 , X3 = on) P( X5 = true| x4 ) ∑ x1 ,x2 ,x3 ,x4 P( x1 ) P( x2 | x1 ) P( x3 | x1 ) P( x4 | x2 , x3 ) P( X5 = true| x4 ) These expressions can often be simplified in the ways that reflect the structure of the network itself.
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