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Introduction to Imprecise Probabilities by Thomas Augustin, Gert de Cooman, Frank P. A. Coolen, Matthias C. M. Troffaes

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10.7 Scoring the conditional probability of the class

If the final aim is to approximate the conditional information of the class c10-math-0407 given the attributes instead of optimizing the accuracy, then a different measure should be used. If conditioned to the attributes, what we obtain is a precise probability for the probability of the class c10-math-0408, then the usual score for each case is the logarithm of the likelihood score: c10-math-0409, where c10-math-0410 is the true value of the class. This scored is added for the different cases in the test set. If instead of a single probability, c10-math-0411, what we obtain is a credal set c10-math-0412, then there is not an obvious way of generalizing this score. Here we propose to use the following one: Let c10-math-0413 the probability having maximum entropy in , then we use the logarithm of the likelihood score computed with ...

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