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For the binary prevalence quantification problem under prior probabilityshift, we determine the asymptotic variance of the maximum likelihoodestimator. We find that it is a function of the Brier score for the regressionof the class label on the features under the test data set distribution. Thisobservation suggests that optimising the accuracy of a base classifier, asmeasured by the Brier score, on the training data set helps to reduce thevariance of the related quantifier on the test data set. Therefore, we alsopoint out training criteria for the base classifier that imply optimisation ofboth of the Brier scores on the training and the test data sets.

Minimising quantifier variance under prior probability shift