Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

(W=-1) (W= 0) (W= 1) (W= 2)
ciS• P r (X) P A rA
(X) P (X) P (X)
rA rA
.5 .5 .73 .50 .27 .119
.1 .9 .23 , .10 .04 .013
.2 .8 . .40 .20 ' .08 . .033
.3 .7 .54 .30 .14 .054
.4 .6 .65 .40 .20 .083 -
.6 .4 .80 .60 .36 .170
.7 .3 . .86 .70 .45 .240
.8 .2 .92 .80 .60 .350
.9 • .1 .96 .90 .77 .550
At first glance it appears that the a priori
probabilities are very important for the model to function.
For instance, a vector of independent variables yielding a
W of 1 will yield aP r (X) of .04 if the a priori probability
A
for air is .1; whereas the same observation will yield a
P r (X) of .77 if q •= .9. However, these are not the
A
A'
necessary probabilities for proper classification.
It can be recognized that the correct value of
the a priori probabilities are only needed for "true"
predicted probabilities of air movement -- but is not
necessary for classification purposes. This can be
seen by looking across the above table. For any given
a priori probability the value of the discriminant (the P r (X) )
A
•
will always give higher numerical probabilities as W •
71.