Dealing with unequal priors in both linear discriminant analysis (LDA) based on Gaussian distribution (GDA) and in Fisher’s linear discriminant analysis (FDA) is frequently used in practice but almost described in neither any textbook nor papers. This is one of the first papers exhibiting that GDA and FDA yield the same classification results for any number of classes and features. We discuss in which ways unequal priors have to enter these two methods in theory as well as algorithms. This may be of particular interest if prior knowledge is available and should be included in the discriminant rule. Various estimators that use prior probabilities in different places (e.g. prior-based weighting of the covariance matrix) are compared both in theory and by means of simulations.

中文翻译：

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线性判别分析中的不等先验

在基于高斯分布 (GDA) 的线性判别分析 (LDA) 和费舍尔的线性判别分析 (FDA) 中处理不等先验在实践中经常使用，但几乎没有在任何教科书或论文中描述。这是第一篇展示 GDA 和 FDA 对任意数量的类别和特征产生相同分类结果的论文之一。我们讨论了在理论上和算法中不等先验必须以何种方式进入这两种方法。如果先验知识可用并且应包含在判别规则中，则这可能特别有趣。在不同地方使用先验概率的各种估计器（例如，协方差矩阵的基于先验的加权）在理论上和通过模拟进行了比较。