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326 13 Inductive vs. Deductive Reasoning The probability on intervals or regions. For example, a temperatureT defines events su ...

13.3 Intensional Approaches to Uncertainty 327 Note that whenPr(B)=0, every number between 0 and 1 is a conditional probability ...

328 13 Inductive vs. Deductive Reasoning know how often the symptom occurs when a person has the disease, then one knowsPr(B|A). ...

13.3 Intensional Approaches to Uncertainty 329 variables satisfy various simplifying properties. The most common simplifi- catio ...

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14 Bayesian Networks Stochastic modeling has a long history, and it is the basis for the empiri- cal methodology that has been u ...

332 14 Bayesian Networks 14.1 The Bayesian Network Formalism ABayesian networkis a graphical formalism for specifying a stochast ...

14.1 The Bayesian Network Formalism 333 Figure 14.1 Example of a BN for medical diagnosis. Rectangles represent discrete random ...

334 14 Bayesian Networks not(PF) PF not(Flu) and not(Cold) 0.99 0.01 not(Flu) and (Cold) 0.90 0.10 (Flu) and not(Cold) 0.10 0.90 ...

14.2 Stochastic Inference 335 causality. In particular, the concern was to distinguish causality from corre- lation. A number of ...

336 14 Bayesian Networks Event A Pr(A) PF and not(Flu) and not(Cold) (0.9999)(0.99)(0.01) = 0.0099 PF and not(Flu) and (Cold) (0 ...

14.2 Stochastic Inference 337 Figure 14.2 Example of diagnostic inference using a BN. The evidence for diagnosis is the percepti ...

338 14 Bayesian Networks Event A Pr(PF and A) not(Flu) and not(Cold) (0.9999)(0.99)(0.01) = 0.0099 not(Flu) and (Cold) (0.9999)( ...

14.2 Stochastic Inference 339 Figure 14.3 Various types of inference. Although information about any of the nodes (random variab ...

340 14 Bayesian Networks The techniques above are concerned with the specification of PDs. A CPD is a function from the possible ...

14.3 Constructing Bayesian Networks 341 Summary The main use of BNs is for stochastic inference. BN inference is analogous to t ...

342 14 Bayesian Networks Machine learning. The PDs and CPDs are most commonly found by us- ing statistical methods. There are a ...

14.3 Constructing Bayesian Networks 343 understood. BN interfaces are discussed in subsection 14.3.3. In most cases, BN developm ...

344 14 Bayesian Networks Figure 14.4 Bayesian network for the result of a research study of body mass index (BMI) as a function ...

14.3 Constructing Bayesian Networks 345 jective, it is helpful to include it in the estimation. As the amount of data and learni ...