By Dawn E. Holmes

Bayesian networks at the moment offer probably the most speedily turning out to be components of analysis in desktop technological know-how and records. In compiling this quantity we have now introduced jointly contributions from the most prestigious researchers during this box. all the twelve chapters is self-contained.

Both theoreticians and alertness scientists/engineers within the extensive sector of man-made intelligence will locate this quantity priceless. It additionally presents an invaluable sourcebook for Graduate scholars because it exhibits the path of present research.

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**Extra resources for Innovations in Bayesian Networks: Theory and Applications**

**Sample text**

We also use p(x|ξ) to denote the probability distribution for X (both mass functions and density functions). Whether p(x|ξ) refers to a probability, a probability density, or a probability distribution will be clear from context. We use this notation for probability throughout the paper. A summary of all notation is given at the end of the chapter. Returning to the thumbtack problem, we deﬁne Θ to be a variable3 whose values θ correspond to the possible true values of the physical probability. We sometimes refer to θ as a parameter.

On what scale should probabilities be measured? In particular, it makes sense to assign a probability of one (zero) to an event that will (not) occur, but what probabilities do we assign to beliefs that are not at the extremes? Not surprisingly, these questions have been studied intensely. , Ramsey 1931, Cox 1946, Good 1950, Savage 1954, DeFinetti 1970). It turns out that each set of properties leads to the same rules: the rules of probability. Although each set 36 D. Heckerman Fig. 1. The probability wheel: a tool for assessing probabilities of properties is in itself compelling, the fact that diﬀerent sets all lead to the rules of probability provides a particularly strong argument for using probability to measure beliefs.

For example, Howard and Matheson (1981), Olmsted (1983), and Shachter (1988) developed an algorithm that reverses arcs in the network structure until the answer to the given probabilistic query can be read directly from the graph. In this algorithm, each arc reversal corresponds to an application of Bayes’ theorem. Pearl (1986) developed a message-passing scheme that updates the probability distributions for each node in a Bayesian network in response to observations of one or more 3 A Tutorial on Learning with Bayesian Networks 47 variables.