Introduction to Bayesian Networks
Introduction to Bayesian Networks
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
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The use of Bayesian methods as both an information combination scheme and an updating tool has become widespread, combining or updating prior information with existing information about events. Bayesian methods stem from the application of Bayes' theorem in probability. As will be noted in this chapter, not only do these methods provide ways of handling various kinds of uncertainties, but they also can serve as a link between subjective-based probability theory and fuzzy logic.In the Bayesian paradigm, uncertainty is quantified in terms of a personal or subjective probability following the axioms of probability theory (see Chapter 3, section 3.2.5), The probability of an event X is denoted P (X; H), where H represents the assessor's information, often called the prior information. Prior refers to the knowledge that exists prior to the acquisition of information about event X. Uncertainties combine via rules of probability that stem from the axiomatic behavioristic interpretation of probability (see Chapter 3, section 3.1). The fundamental Bayesian philosophy is that prior information, H, is valuable and can be mathematically combined with information about X and, with such combination, uncertainties can be reduced.Understanding the uses of Bayesian methods begins with the historical development of the theory.