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61.182 Informaatiotekn. ek II, spring 1997

Exercise problems

(Ch. 4, Ripley)

9. Here is a part of the "medical diagnosis" graph of Ripley, p. 270, and all the related probabilities. Using just the Bayes rule, what would be the probability of a) heart disease, b) breathlessness for a person, who does not smoke, but who has a family history of heart disease.

Figure 1: The DAG for an artificial medical diagnosis system.


Pr{A}=0.5 Pr{B} = 0.2 Pr{C}=0.3
Pr{D | F,F}=0.05 Pr{D | F,T}=0.3 Pr{D | T,F }=0.2 Pr{D | T,T} = 0.5
Pr{E | F}=0.3 Pr{E | T} = 0.5
Pr{F | F} = 0.1 Pr{F | T}=0.4
Pr{G | F,F}=0.01 Pr{G | F,T}=0.5 Pr{G | D=T}=1
Table 1: The conditional probability tables for the DAG of Fig. 1. For each vertex the condition is on its parents in alphabetical order.

(Ch. 9, Ripley)

10. Jones and Sibson introduced a Projection Pursuit index based on moments:




are the skewness and the kurtosis of the projection tex2html_wrap_inline76 . Here x is the multidimensional zero-mean data vector, a is the projection direction, and tex2html_wrap_inline82 is expectation.

You wish to find the direction a that will maximize this index. Device a suitable algorithm.

Esa Alhoniemi
Fri Apr 11 10:27:45 DST 1997