统计研究

判别分析是三大多元统计分析方法之一,在许多领域都有广泛的应用。通常认为距离判别、Fisher判别和Bayes判别是三种不同的判别分析方法,本文的研究表明,距离判别与Bayes判别是两种实质的判别方法,前者实际依据的是百分位点或置信区间,后者实际依据的是概率。而著名的Fisher判别,只是依据方差分析的思想,对判别变量进行线性变换,然后用于距离判别,其实不能算是一种实质的判别方法。本文将Fisher变换与Bayes判别结合起来,即先做Fisher变换,再利用概率最大原则做Bayes判别,得到一种新的判别途径,可进一步提高判别效率。理论与实证分析表明,基于Fisher变换的Bayes判别,适用场合广泛,判别效率最高。

It is commonly accepted that distance discrimination,Fisher discriminant and Bayes discriminant are different methods.This paper argues that distance discriminant and Bayes discriminant method are two discriminant methods in essential,but Fisher discriminant method,based on the idea of ANOVA,makes linear transformation of variables and thus can not be considered as a kind of discriminant method in essential.This paper tried to combine Fisher discriminant method and the Bayes discriminant method,that is,firstly make Fisher transformation,then use the principles of Bayesian probability in order to improve the efficiency of discrimination.