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Hayes Network

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Hayes Network. Incidences of diseases A and E (DA, DE) depend on the exposure (E). Disease A is additionally in?uenced by risk factors (R). Both diseases lead to symptoms (S). Results of the test for disease A [T3] are affected also by disease E. Positive test wi? be denoted as TA 2 1, negative as TA 2 (l. The Hayes Network is shown in Figure I. Needed conditional probabilities are shown in Table l. 9 9 ® a Figure 1: The DAG of the Bayesian networks Table 1: The known (or elicited) conditional probabilities E I) l R [I 1 I13 0.2 [LT {1.3 DB III] 1 E” {1.8 {1.2 E [1.3 [LT 0.95 [1.05 3313‘}; 0.92 0.08 ???g 0.5 0.4 BEBE {1.3 0.2 BABE. 0.4 0.5 343% [1.15 0.35 BABE 0.1 0.9 DAD}; DIE $.97 [a] 1What is the probability of disease A [DA 2 1}, if disease B is not present (DB 2 III}, but symptoms are present (8 = l}. (b) What is the probability of exposure (E = 1}I if symptoms are present {5' = 1} and test is positive [TA = 1). Hint: You can solve this problem by any of the 3 ways: {i} use of WinEUGS or Open—

BUGS, (ii) direct simulation using Octave/MATLAB, R, or Python, and (iii) exact calcula- tion.