多元统计分析第05章.pdf

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1、1?!?O?1?!?O?June 11,20031?!?O?O?u?a.?O?X13?,?fik?5?U?U?U,k?.23L,?I!?!?Y?I5?I?Lu?a.33|?N?I?eG?!?1?!?O?3=?+?,?O?flK?:?kk?m?oNG1,G2,Gk,?A?fi?(Xfi?O?F1(x),F2(x),Fk(x),?5g?oN?).?#?X,?5g=?oN.A?O?k:?l?O!Bayes?O!Fisher?O!?O!S0?O?.1?!?O?5.1?l?O5.1?l?O?l?O?g?:?=?oN?l?C,?u=?oN.?l?O?*?O.1?!?O?5.1?l?O?!?l?!?lllf

2、i?k?aG1?G2,XG1?A)?,G2?B)?a?.?A?p,?F?(1)=80,?N?21=0.25;?B,?F?(2)=75,?22=4.8k?X0,?F?(0)=78,?T?5g=?oN?*?X0?A)?,e?5?l.PX0?G1?G2?l?d21(x)?d22(x),Kd21(x0)=(x0(1)221=(78 80)20.25=16d22(x0)=(x0(2)222=(78 75)24.00=2.25dud22(x0)d21(x0),?X0?B)?n.1?!?O?5.1?l?O?!?l?,?b?oNG1?N(1),21),oNG2?N(2),22),K|?l?.:(b?(1)X

3、G2,x 1?!?O?5.1?l?O?!?l?m?oN?l?(5.1.1)?oNG?m?oN,?=(1,2,m)0,?=(ij)mm,K?X?oNG?l?d2(X,G)=(X )01(X )1?!?O?5.1?l?O?!?oN?l?O?!?oooNNN?lll?OOO0.?VVVggg?k?oNG1?G2,5gGi?X(i)(t)=(x(i)(t1),(i)(t2),(i)(tm)0i=(1,2);t=(1,2,ni),K?O?X(i)=(1niniXt=1x(i)t1,1niniXt=1x(i)tm)0=(x(i)1,x(i)2,X(i)m)0oNG?i?OSi(?|SSS?)?Si=1ni

4、 1Ai=(s(i)lj)mm1?!?O?5.1?l?O?!?oN?l?O?Ai=niXt=1(X(i)(t)X(i)(X(i)(t)X(i)0?|Sl?s(i)lj=1ni 1niXt=1(x(i)tl x(i)(x(i)tj x(i)(l,j)=(1,m)1?!?O?5.1?l?O?!?oN?l?O?b1=2=?,?O?S=1n kkXi=1Ai=(slj)mmS?slj=1n k2Xi=1niXt=1(x(i)tl x(i)(x(i)tj x(i)(l,j)=(1,m)1?!?O?5.1?l?O?!?oN?l?O1.1=2?OOO?O?X?oN?ld2(X,G1)?d2(X,G2),?O

5、OK?:(X G1,d2(X,G1)0X G2,W(X)0W(X)?5?O.1?!?O?5.1?l?O?!?oN?l?O?m=1?A?,?oN?oN,?N(1),2)?N(2),2),?O?W(x)=(x 12(1)+(2)2(1)(2)PP(2|1)L?uG1?G2?V.O?P(2|1)=P(1|2)=1 (1)(2)2)?oN?C?,?V?,?O?v,?k?oN?kw?,?O?k.1?!?O?5.1?l?O?!?oN?l?O2.16=2?OOO?,O?O,-W(X)=d2(X,G2)d2(X,G1)=def=Z(X)Z0?Z(X)?X?g(16=2),Z0?.?OOK?:(X G1,W(X

6、)0X G2,W(X)01?!?O?5.1?l?O?!?oN?l?O?m=1?,?Gi?N(i),2i)(i=1,2).?(1)(2)?l?di(x)=|x (i)|i?*?v(2)x X G2,x 1?!?O?5.1?l?O?!?oN?l?O?m=1?,?Gi?N(i),2i)(i=1,2).?(1)(2)?l?di(x)=|x (i)|i?*?v(2)x X G2,x 1?!?O?5.1?l?O?!?oN?l?O5.1.1(?aaa555?OOO)1?!?O?5.1?l?O?!?oN?l?Osas/stat?discrimL,O?(J?|m?l?37.02876,u?H0:1=2?F?O?

7、14.46436,P=0.0059 0.01,?a?kw?.?5?OY1(X)=42.2473+7.6741X1+5.5488X213.9631X3+1.1813X4Y2(X)=5.1627+2.9311X1+1.3570X25.3738X3+0.4558X4?(J5gA?B?10?,8?(J?:2,3,6,7,8?a?,?.1?!?O?5.1?l?On!oN?l?Onnn!oooNNN?lll?OOO?kk?m?oN:Gii=1,k,?O?(i),i,?X5g=?oN.O?X?oN?ld2i(X)i=1,k?OOK:X Gl,d2l=mini=1,kd2i(X)1?!?O?5.1?l?On!

8、oN?l?Onnn!oooNNN?lll?OOO?kk?m?oN:Gii=1,k,?O?(i),i,?X5g=?oN.O?X?oN?ld2i(X)i=1,k?OOK:X Gl,d2l=mini=1,kd2i(X)1?!?O?5.2 Bayes?O92?l?O5.2 Bayes?O92?l?O?lll?OOO?:1.T?O?oN?y?.2.vk?Bayes?OOOggg?:b?fik?,k?V?5;,?,?5?fik?(k?),?V?.?Bayesg?u?O?Bayes?O?O?,?mRm?y:D=D1,Dk.?yA?O?.Bayes?O?mRm?y.1?!?O?5.2 Bayes?O92?l?

9、O?!k?V(k?)?!kkk?VVV?kk?oN,G1,Gk.b?flk?k?,=fi?k?oN?g?y?V?q1,qk(?cV).|?cVq1,qk?k?V.X?+?J(G1)?vkJw(G2)?a+N?flK,d?:q1=0.001,q2=0.999.k?V?:1|?9?1?O2|?a?oN?ni/n?qi?3bq1=qk=1/k1?!?O?5.2 Bayes?O92?l?O?!k?V(k?)?!kkk?VVV?kk?oN,G1,Gk.b?flk?k?,=fi?k?oN?g?y?V?q1,qk(?cV).|?cVq1,qk?k?V.X?+?J(G1)?vkJw(G2)?a+N?flK,d

10、?:q1=0.001,q2=0.999.k?V?:1|?9?1?O2|?a?oN?ni/n?qi?3bq1=qk=1/k1?!?O?5.2 Bayes?O92?l?O?!2?l?!222?lll?X?oNGt(t=1,k)?2?l?:D2t(X)=D2(X,Gt)=d2t(X)+g1(t)+g2(t),?g1(t)=(ln|St|,e?|?i?0e?|?i?g2(t)=(2ln|qt|,ek?V?0ek?V?2?l?O?:?X Gt,eD2t(X)P(i|X)(i 6=t,i=1,k)1?!?O?5.2 Bayes?O92?l?Oo!?d?OOKooo!?ddd?OOOOOOKKK?ddd?O

11、OOOOOKKK,?mRm?y:D=D1,Dk,?5?.1.?VVV?ruGi?X,?OD?O?%?Gj(j 6=i)(=?)?VP?P(j|i;D)(P?P(j|i).KkP(j|i;D)=ZZDjfi(x1,xm)dx1dxm=ZDjfi(X)dX(j 6=i).1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK?V?O?:1|?u?8,=?O?fi?aO?1?,?O?A?o?2?,3?fi?aO?u?8,?O?3?(?u?),zg3?fi?aO?,?n-1?OOK,?3?fi?aO?1?O8a.?O?91?!?O?5.2 Bayes?O92?l?Oo!?d?OOK?ruGi?

12、X,?OD?O?%?Gj(j 6=i)(=?)?L(j|i;D)L,?eOL(j|i).L(j|i)?D?:1d?D?2b?1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK2.uuukkk?VVV?k?V,?ODuk?V?:g(D)=kXt=1qtkXj=1P(j|t)L(j|t)def=kXt=1qtrt(D)?rt(D)LGt?oN?.1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK3.?ddd(Bayes)?OOOOOOKKK5.2.1?kk?oN:G1,Gk,?A?k?V?q1,qk.XJk?OD,?D?5?,=g(D)=min?Dg(D),K?OD?d?O

13、OK,D?d?O?).1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK4.?ddd?OOOOOOKKK(?ddd?OOO?)nnn5.2.1?kk?oN:G1,Gk,fi?Gi?fi(X),k?V?q1,qk,?L(j|i),K?d?O?)D=D1,Dk?Dt=X|ht(X)qjfj(X),j 6=t,j=1,k(t=1,k),1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK4.?ddd?OOOOOOKKK(?ddd?OOO?)nnn5.2.1?kk?oN:G1,Gk,fi?Gi?fi(X),k?V?q1,qk,?L(j|i),K?d?O?)D=D1,Dk?Dt=X

14、|ht(X)qjfj(X),j 6=t,j=1,k(t=1,k),1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK5.2.1?k=2?d?O?).)h1(X)=q2f2(X)L(1|2)h2(X)=q1f1(X)L(2|1)l?D1=X|q2f2(X)L(1|2)dX G2,W(X)d1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK5.?oooNNN?ddd?OOO?Gi Nm(i),i)(i=1,k),b?,k?V?q1,qk(1)?1=2=mdef=?,oNGi?V?fi(X),Kqifi(X)=qi(2)m/2|1/2exp?12(X (i)01(X (i)?

15、lnqifi(X)=12ln|+mln(2)+X01X+lnqi12(i)01(i)=C0+Ci0+X0Cidef=C0+Yi(X)?C0=12ln|+mln(2)+X01X?Gi?6?X?.Ci0=lnqi12(i)01(i);Ci=1(i)def=(Ci1,Cim)0.1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK?(i)(i=1,k)?,d?O?1i?oN?X(i),?S=1n k(A1+Ak).?d?)D=D1,Dk?Dt=X|Yt(X)Yj(X),j 6=t,j=1,k(t=1,k),?Yt(X)=Cj0+C0jX,?5?O,Cj=S1X(j)?OX,Cj0=lnqi

16、12(X(j)01X(j)?.1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK(2)?i(i=1,k)?lnqifi(X)=d0122lnqi+ln|i|+(X (i)01i(X (i)def=d0+Zi(X)?d0=m2ln(2).?(i),i?,?O?1i?oN?X(i),?Si1?!?O?5.2 Bayes?O92?l?Oo!?d?OOK?d?O?)D=D1,Dk?Dt=X|Zt(X)Zj(X),j 6=t,j=1,k(t=1,k),?Zj(X)=lnqjfj(X)d0=12D2j(X)Zj(X)?g?O.?3?e,?d?O?2?l?O?.1?!?O?5.2 Bayes?O

17、92?l?Oo!?d?OOK5.2.2(?JJJ?OOO)L5.2l?pkn?oN?J!?5?.lz?oN5?z 0?A?v?A?l1,lr,?a=l1?(a)?,?1(a)?OOO?.1?!?O?5.3 F?(Fisher)?O?!?5?O?5.3.1?A1B?A?1 ,r 0?A?v?A?l1,lr,P1=1/rXi=1i?5?Ou1(X)=l01X?OU?;P(l)=(1+l/rXi=1i?cl?(l r)?5?Ou1(X)=l01X,ul(X)=l0lX?OOO?OOOUUU?.1?!?O?5.3 F?(Fisher)?On!Fisher?OOKnnn!Fisher?OOOOOOKKK

18、1.?OOOOOOKKKI(r=1)?XJ?k?Ou(X)=l0X?m?K?5.3.1ek=2,Fisher?5?O9?A?O?.)?oN?|ml?B?B=n1(X(1)X)(X(1)X)0+n2(X(2)X)(X(2)X)01?!?O?5.3 F?(Fisher)?On!Fisher?OOK|X=1n1+n2(n1X(1)+n2X(2)?B=n1n2n1+n2(X(1)X(2)?|Sl?A=A1+A2,?At=ntXi=1(x(t)(i)X(t)(x(t)(i)X(t)0i=1,2duB?u1,?A?|A1B I|=0?A?k?.?A1B=n1n2n1+n2A1(X(1)X(2)(X(1)X

19、(2)0k?5?:AB?BA?A?.A1B?A?u:n1n2n1+n2(X(1)X(2)0A1(X(1)X(2)=n1n2n1+n2d2,1?!?O?5.3 F?(Fisher)?On!Fisher?OOK?d2=(X(1)X(2)0A1(X(1)X(2)?n1n2n1+n2d2?,?A?.Pl?Au?3?l0Al=1?A?,?vBl=Al,?l=1dA1(X(1)X(2)?v?.u?Fisher?5?O?u(X)=1dX0A1(X(1)X(2)?A?O?(l)=n1n2n1+n2(X(1)X(2)0A1(X(1)X(2)1?!?O?5.3 F?(Fisher)?On!Fisher?OOKek

20、=2?U?lOK?O?8a?O.?oN?X(1)?X(2),?5?O?(1)=l0X(1),(2)=l0X(2)e?K?oN?,KK?:=12(l0X(1)+l0X(2)e?K?oN?,KK?:=2(1)+1(2)1+2?t?K?oNGt?,?t=l0Stl1?!?O?5.3 F?(Fisher)?On!Fisher?OOK?OOK?(?l0X(1)l0X(2)X G1u(X)()X G2u(X)1)?k?O?(P?1)?5?Ou1(X)=l01X,k?oN?3l1?K?u(t)1=l01X(t)t=1,k?X,O?3l1?K:e?3?i1,|u1(X)u(i1)1|(i1)=mint=1,k

21、|u1(X)u(t)1|t?,?X Gi1.XJ?3j?oNGk1,Gkj,?u1(X)?l?,PS?8L=k1,kj,K2?O?2(g?)?Ou2(X)=l02X,1?!?O?5.3 F?(Fisher)?On!Fisher?OOK?3?i2,|u2(X)u(i2)2|(i2)=mintL|u2(X)u(t)2|t?,?X Gi2.?u(t)2=l02X(t)XJ1?OE?U?O?XoN,K?1n?5?O,?da?.?OK/?S0?O?g?.1?!?O?5.3 F?(Fisher)?On!Fisher?OOK3.?OOOOOOKKKIIIXJkr?A?,?A?kr?5?Ou1(X),ur(X)?ur?5m?C?n?r?#C?.3?l r,?vlXi=1i/rXi=1i P0(p0?0.7)?m?oN?OflK=z?l?oN?OflK,?l?#C?p?,?U?l?OOK58a.