New PDF release: Bayesian Networks and Decision Graphs

By Finn V. Jensen (auth.)

ISBN-10: 1475735022

ISBN-13: 9781475735024

ISBN-10: 1475735049

ISBN-13: 9781475735048

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Additional info for Bayesian Networks and Decision Graphs

Example text

Let A have n states with P(A) = (Xl, ... ,xn ), and assume that we get the information e that A can only be in state i or j. This statement expresses that all states except i and j are impossible, and we have the probability distribution P(A, e) = (0, ... ,0, Xi, 0, ... ,0, Xj, 0, ... ,0). Note that P(e), the prior probability of e, is the sum of P(a, e). Note also that P(A, e) is the result of multiplying P(A) with (0, ... ,0,1,0, ... ,0,1,0, ... ,0), where the 1's are at the ith and jth places.

P(Child I Father, Mother) for genetic inheritance. The numbers (a, {3, 'Y) are the child's probabilities for (aa, aA, AA). 48 2. 4. However, for all horses except John, we have additional knowledge. Since they are in production, they cannot be of type aa. A way to incorporate this would be to build a Bayesian network where all inheritance is modeled in the same way and afterward enter the findings that all horses but John are not aa. It is also possible to calculate the conditional probabilities directly.

While Angina? has an impact on all information variables. 5. 5. A model for Cold or angina? The next thing to check is whether the conditional independencies laid down in the model correspond with reality. , then seeing spots will not have an impact on the expectation either for Fever? or for Sore Throat? If we do not agree, we may introduce a link from See Spots? to, for example, Fever? For now, we will accept the conditional independencies given by the model. 3 Insemination Six weeks after insemination of a cow, there are two tests for the result: blood test (BT) and urine test (UT).

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Bayesian Networks and Decision Graphs by Finn V. Jensen (auth.)


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