For the binary prevalence quantification problem under prior probability shift, we determine the asymptotic variance of the maximum likelihood estimator. We find that it is a function of the Brier score for the regression of the class label against the features under the test data set distribution. This observation suggests that optimising the accuracy of a base classifier on the training data set helps to reduce the variance of the related quantifier on the test data set. Therefore, we also point out training criteria for the base classifier that imply optimisation of both of the Brier scores on the training and the test data sets.

翻译：对于在先前概率变化情况下的二元流行程度量化问题,我们确定最大概率估计值的无症状差异。我们发现,这是Brier分数相对于测试数据集分布下分类标签特征回归的函数。这一观察表明,在培训数据集上优化基准分类员的准确性有助于减少测试数据集中相关限定值的差异。因此,我们还指出了基准分类师的培训标准,这意味着在培训和测试数据集中优化Brier分数。