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Given baseline hypothesis H0, we now show Pwin of Hi in subdomain j with respect to the average performance of H0. Assuming sample mean Ȑˆ i, j, sample variance ␴ˆ i,2 j, and ni, j test cases, Pwin is defined as follows:  Pwin (i, j) = Ft ni, j − 1, µ ˆ i, j σˆ i,2 j /ni, j   (8) where Ft(␯, x) is the cumulative distribution function of Student’s t-distribution with ␯ degrees of freedom, and Pwin(i, j) is the probability that the true performance (population mean) of Hi in subdomain j is better than that of H0.

The primary advantages of graphical probabilistic models is that they are perhaps some of the most natural and computationally feasible ways devised yet for managing uncertainty. The representation is visually appealing, the inference mechanisms have a solid statistical and probabilistic foundation, and the approach is a very flexible method for representing beliefs about what factors influence others, and to what extent. In the past, belief maintenance systems based on probability modeling were viewed as being too impractical to use.

The changes in the node are isolated from the rest of the network by working entirely within the Markov blanket of the node in question. The Markov blanket of node Xi consists of the parents and children of Xi, and the parents of the children of Xi. See Chang and Fung (23) for more details. Sensitivity analysis is another area of interest to belief network analysis. The idea is to vary certain assumptions about the domain, and measure how much the output of the system varies. One could vary the class of distribution that is being used, assumptions about which variables influence others, the type or strength of the prior distribution, or the input values.

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31.Knowledge and Data Engineering by John G. Webster (Editor)

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