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R ( a i |x ) = ∑ L a i |w j Pr ( w j | x )
j= i
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a if R ( a1 |x ) < R(a 2 | x)
decide  1
else.
a 2
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R ( a1 |x ) = Pr ( w1 |x ) L11 + Pr ( w 2 |x ) L12
R ( a 2 |x ) = Pr ( w1 |x ) L 21 + Pr ( w 2 |x ) L 22
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Pr ( w1 |x ) L 21 + Pr ( w 2 |x ) L 22 > Pr ( w1 |x ) L11 + Pr ( w 2 |x ) L12
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Pr ( w1 |x )
Pr ( w 2 |x )
>
(L12 − L 22 )
(L 21 − L11 )
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Pr ( w1 |x ) >
(L12 − L 22 )
=
(L 21 − L11 ) + (L12 − L 22 )
1
 L − L11 
1 +  21
 L12 − L 22 
.
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)(6);$6(+$+($-#$9(6),8#'#8h+"#$2-(4#$,6#1&2/,+3$926$-#$),5%/,*,#8$+($+"#$*(//(7,60;$
7",9"$,)$+"#$*('5$2)$,+$72)$(',0,62//3$&)#8$-3$Y2%/26$,6$",)$)#5,62/$JKL[$%2%#'UW[
Pr ( w1 |x ) >
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=
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1
.
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1+ 
 L12 
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62/$92)#);$268$+"#$I/(7#'N$)+2682'8$(*$F%'#%(68#'269#$(*$+"#$#4,8#69#H$IF-2/269#$(*$
%'(-2-,/,+,#)H$,6$:60/,)"$/27N$,6$9,4,/$92)#)<\M$!($'#29"$2$0&,/+3$4#'8,9+$,6$2$9',5,62/$
92)#;$+"#$P&'3$5&)+$-#$9(64,69#8$-#3(68$263$'#2)(62-/#$8(&-+$+"2+$+"#$*29+)$2//#0#8$
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202,6)+$+"#$8#*#6826+<\J
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