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44 DETECTION AND CLASSIFICATION
5. What quantities do you need to compute the Bayes classifier? How would you obtain
these quantities? (0)
6. Derive a decision function assuming that objects come from normally distributed
classes as in Section 2.1.2, but now with an arbitrary cost function ( ).
7. Can you think of a physical measurement system in which it can be expected that the
class distributions are Gaussian and where the covariance matrices are independent
of the class? (0)
8. Construct the ROC curve for the case that the classes have no overlap, and classes
which are completely overlapping. (0)
9. Derive how the ROC curve changes when the class prior probabilities are changed. (0)
10. Reconstruct the class conditional probabilities for the case that the ROC curve is not
symmetric around the axis which runs from (1,0) to (0,1). (0)
