第五章数据分析（梅长林）习题.doc

1、第五章数据分析p （梅长林）习题第五章习题 1.习题5.1 解：假定两总体服从正态分布，且协方差矩阵，误判损失相同又先验概率按比例分配，通过SAS计算得到先验概率如表：Class Level Information group Variable Name Frequency Weight Proportion Prior Probability G1 G1 6 6.0000 0.428571 0.428571 G2 G2 8 8.0000 0.571429 0.571429 即：又计算可得：有计算的总体协防差距矩阵S为：Pooled Within-Class Covariance Matri_

2、, DF = 12 Variable _1 _2 _1 1.081944444 -0.310902778 _2 -0.310902778 0.174756944 并且：计算广义平方距离函数：并计算后验概率：回代判别结果如下: Posterior Probability of Membership in group Obs From group Classified into group G1 G2 1 G1 G1 0.9387 0.0613 2 G1 G1 0.9303 0.0697 3 G1 G1 0.9999 0.0001 4 G1 G2 _0.4207 0.5793 5 G1 G1 0.

3、9893 0.0107 6 G1 G1 1.0000 0.0000 7 G2 G2 0.0007 0.9993 8 G2 G2 0.0026 0.9974 9 G2 G2 0.0008 0.9992 10 G2 G2 0.0586 0.9414 11 G2 G2 0.0350 0.9650 12 G2 G2 0.0006 0.9994 13 G2 G2 0.0038 0.9962 14 G2 G2 0.0012 0.9988 由此可见误判的回代估计：若按照交叉确认法，定义广义平方距离如下：逐个剔除, 交叉判别，后验概率按下式计算：通过SAS计算得到表所示结果。发现同样也是属于G1的4号被误判为

4、G2，因此误判率的交叉确认估计为 Posterior Probability of Membership in group Obs From group Classified into group G1 G2 1 G1 G1 0.9060 0.0940 2 G1 G1 0.7641 0.2359 3 G1 G1 1.0000 0.0000 4 G1 G2 _0.1950 0.8050 5 G1 G1 0.9743 0.0257 6 G1 G1 1.0000 0.0000 7 G2 G2 0.0012 0.9988 8 G2 G2 0.0051 0.9949 9 G2 G2 0.0014 0.9

5、986 10 G2 G2 0.0713 0.9287 11 G2 G2 0.0422 0.9578 12 G2 G2 0.0009 0.9991 13 G2 G2 0.0059 0.9941 14 G2 G2 0.0022 0.9978 其中=12.1138， ，又因为，所以， 最后可得后验概率p为：0.048709 习题5.3 解：（1）在并且先验概率相同的的假设前提下，建立矩离判别的线性判别函数。利用SAS的proc discrim过程首先计算得到总体的协方差矩阵，如表：Pooled Within-Class Covariance Matri_, DF = 25 Variable _1 _

6、2 _3 _4 _5 _6 _7 _8 _1 2.25705591 -0.91513311 0.34259974 -0.6084399 -0.9576508 -0.8929719 -0.0539445 -0.2192724 _2 -0.9151331 25.2318255 -0.3390873 -2.5515272 -5.0966371 0.78571637 -0.0835586 4.37529806 _3 0.34259974 -0.33908734 3.30063123 1.42276017 1.78692343 0.40208409 -0.0676655 -0.0732213 _4 -0

7、.6084399 -2.55152726 1.42276017 6.07845863 5.78100857 2.32331 -0.3205116 0.48605897 _5 -0.9576508 -5.09663714 1.78692343 5.78100857 8.15854743 3.44983429 -0.1096651 0.08904743 _6 -0.8929719 0.78571637 0.40208409 2.32331 3.44983429 4.16657066 -0.2236278 0.87862549 _7 -0.0539445 -0.08355869 -0.0676655

8、 -0.3205116 -0.1096651 -0.2236278 0.26009291 -0.0767347 _8 -0.2192724 4.37529806 -0.0732213 0.48605897 0.08904743 0.87862549 -0.0767347 2.51054423 各个总体的马氏平方距离见表：Generalized Squared Distance to group From group G1 G2 G1 0 24.61468 G2 24.61468 0 线性判别函数为：得到训练样本回判法判别结果如表：Error Count Estimates for group

9、G1 G2 Total Rate 0.0000 0.0000 0.0000 Priors 0.5000 0.5000 训练样本的交叉确认判别结果：Posterior Probability of Membership in group Obs From group Classified into group G1 G2 17 G1 G2 _0.4501 0.5499 19 G1 G2 _0.0920 0.9080 Error Count Estimates for group G1 G2 Total Rate 0.1000 0.0000 0.0500 Priors 0.5000 0.5000

10、（2）假设两总体服从正态分布，先验概率按比例分配且误判损失相同，在两总体协方差矩阵相同，即的条件下进行Bayes判别分析p ，通过SAS discrim过程得到结果：Error Count Estimates for group G1 G2 Total Rate 0.0000 0.0000 0.0000 Priors 0.7407 0.2593 交叉确认判别结果：Posterior Probability of Membership in group Obs From group Classified into group G1 G2 19 G1 G2 _0.2246 0.7754 25 G2

11、 G1 _0.5282 0.4718 Error Count Estimates for group G1 G2 Total Rate 0.0500 0.1429 0.0741 Priors 0.7407 0.2593 在，并且先验概率按比例分配的假设前提下利用SAS的proc discrim过程进行Bays判别分析p ，这时以个总体的训练样本单独估计各总体的协方差矩阵，可到的训练样本的回判和交叉确认结果：回判结果：Error Count Estimates for group G1 G2 Total Rate 0.0000 0.0000 0.0000 Priors 0.7407 0.2593

12、 交叉确认判别结果：Posterior Probability of Membership in group Obs From group Classified into group G1 G2 21 G2 G1 _1.0000 0.0000 22 G2 G1 _1.0000 0.0000 23 G2 G1 _1.0000 0.0000 24 G2 G1 _1.0000 0.0000 25 G2 G1 _1.0000 0.0000 26 G2 G1 _1.0000 0.0000 27 G2 G1 _1.0000 0.0000 Error Count Estimates for group G1

13、 G2 Total Rate 0.0000 1.0000 0.2593 Priors 0.7407 0.2593 （3）在不同的假设前提，采用不同判别方法得到待判样本的判别结果：1.距离判别分析p 得到、上海、广东的判别结果：Posterior Probability of Membership in group Obs Classified into group G1 G2 1 G2 0.0000 1.0000 2 G2 0.0000 1.0000 3 G2 0.0000 1.0000 2.在协方差矩阵相同的前提下，Bayes对、上海、广东的判别结果：Posterior Probabilit

14、y of Membership in group Obs Classified into group G1 G2 1 G2 0.0000 1.0000 2 G2 0.0000 1.0000 3 G2 0.0000 1.0000 3在协方差不同矩阵相同的前提下，Bayes对、上海、广东的判别结果：Posterior Probability of Membership in group Obs Classified into group G1 G2 1 G1 1.0000 0.0000 2 G1 1.0000 0.0000 3 G1 1.0000 0.0000 3.习题5.4 解：（1）假设两总体

15、服从正态分布且在两总体协方差矩阵相同，即，先验概率按相同的条件下进行Bayes判别分析p ，通过SAS discrim过程得到结果：首先得到线性判别函数：回代误判结果：Posterior Probability of Membership in group Obs From group Classified into group G1 G2 9 G1 G2 _0.3401 0.6599 29 G2 G1 _0.8571 0.1429 由计算结果发现，第9号样本被误判到G2,29号样本被误判到G1.误判率为6.34 Error Count Estimates for group G1 G2 To

16、tal Rate 0.0833 0.0435 0.0634 Priors 0.5000 0.5000 交叉确认判别结果：由计算发现总共有四个样本被判错，分别是9、28、29、35号样品。累计误判率为10.69 Posterior Probability of Membership in group Obs From group Classified into group G1 G2 9 G1 G2 _0.0973 0.9027 28 G2 G1 _0.6130 0.3870 29 G2 G1 _0.9643 0.0357 35 G2 G1 _0.8470 0.1530 Error Count

17、Estimates for group G1 G2 Total Rate 0.0833 0.1304 0.1069 Priors 0.5000 0.5000 （1）假设两总体服从正态分布且在两总体协方差矩阵相同，即，先验概率按比例分配且误判损失相同的条件下进行Bayes判别分析p ，通过SAS discrim过程得到结果：首先得到线性判别函数：Linear Discriminant Function for group Variable G1 G2 Constant -99.91796 -95.41991 _1 30.35060 29.87680 _2 -0.15214 -0.15210 _3

18、 -0.78868 -0.22662 _4 1.95176 1.39528 _5 0.58964 0.06490 _6 -108.95 -85.33735 _7 -0.31156 -0.25957 回代误判结果 Posterior Probability of Membership in group Obs From group Classified into group G1 G2 9 G1 G2 _0.2119 0.7881 29 G2 G1 _0.7579 0.2421 Error Count Estimates for group G1 G2 Total Rate 0.0833 0.0435 0.0571 Priors 0.3429 0.6571 交叉确认误判结果：Posterior Probability of Membership in group