T t a ba a wa 1 w b x j t j a x t a x

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T T a Ba a Wa 1 W B x j T j a x T a x
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江西财经大学 统计学院 10.4 Bayes discriminant analysis The idea of Bayes discriminant analysis Introduce The Principle
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江西财经大学 统计学院 一个好的判别方法,既要考虑到各个总体出现 的先验概率,又要考虑到错判造成的损失,贝叶斯 (Bayes) 判别就具有这些优点,其判别效果更加理 想,应用也更广泛。 贝叶斯公式是一个我们熟知的公式 ) ( ) | ( ) ( ) | ( ) | ( i i i i i B P B A P B P B A P A B P 距离判别简单直观,很实用,但是距离判别 的方法把总体等同看待,没有考虑到总体会以不 同的概率 ( 先验概率 ) 出现,也没有考虑误判之后 所造成的损失的差异。
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江西财经大学 统计学院 ) ( ) ( ) | ( 0 0 0 x f q x f q x G P j j i i i ) ( ) ( ) | ( 0 0 0 x f q x f q x G P j j l l l ) ( ) ( 0 0 1 max x f q x f q j j i i k i 判给 ,在正态的假定下, 为正态分布的 密度函数。 0 x l G ) ( x f i 设有总体 具有概率密度函 。并且根据以往的统计分析,知道 出现的概 率为 。即当样本 发生时,求 属于某类的概率。 由贝叶斯公式计算后验概率,有: i G ) ( x f i i G i q 0 x ) , , 2 , 1 ( k i G i 0 x 判别规则
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江西财经大学 统计学院 考虑错判损失的 Bayes 判别分析 设有总体 具有概率密度函 。并且根据以往的统计分析,知道 出现 的概率为 i G ) ( x f i i G i q ) , , 2 , 1 ( k i G i ) 1 ( 1 k q q D 1 D 2 D k R (p) 的一个分划,判别法则为: 关键的问题是寻找 D 1 D 2 D k 分划,这 个分划应该使平均错判率最小。 i D X k i , , 3 , 2 , 1 当样品 X 落入 D i 时,判
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江西财经大学 统计学院 【定义】 (平均错判损失) j D i i j dx x f G D X P i j p ) ( ) / ( ) / ( j i C(j/i) 表示相应错判所造成的损失。 则平均错判损失为: k i i j i i j P i j C q ECM 1 ) / ( ) / ( 使 ECM 最小的分划,是 Bayes 判别分析的解。 表示将来自总体 G i 的样品错判到总体 G j 的条件概率。 ) / ( i j p
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江西财经大学 统计学院 The idea of Bayes discriminant analysis This kind of information can usually be utilized to form a prior probability distribution. According to the principle of Bayes’ rule, the prior distribution can possibly be further refined after obtaining the observations, and refined to form the posterior distribution. The discriminant involving the posterior distribution is often referred to as Bayes discriminant.
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江西财经大学 统计学院 Introduce The Principle Assume that each set has a density function where . We already know that the prior probability distributions are respectively.
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