ties are defined as below,

݌஺ൌ

ߨ஺݂஺

ߨ஺݂஺൅ߨ஻݂஻

݌஻ൌ

ߨ஻݂஻

ߨ஺݂஺൅ߨ஻݂஻

(3.15)

two posterior probabilities have the properties, 0 ൑݌஺, ݌஻൑1

݌஻ൌ1. Using these two probabilities, the Bayes rule is defined

ܼൌ൜^ܣ

݌஺൐݌஻

ܤ

݌஺൑݌஻

(3.16)

ܼൌ൜^ܣ

݌஺൐0.5

ܤ

݌஺൑0.5

(3.17)

stance, the inset at the bottom-right corner of Figure 3.2 is a good

to show the relationship between two posterior probabilities (݌஺

The height sum at each point of this posterior probability curve

will always be one. In this inset, the pattern of three validation

learly shows the relationship between ݌஺ and ݌஻. For the

n point B which is one member of the triangle class, it can be seen

osterior probability in the solid line (for the triangle class) is

ne, but its posterior probability in the dotted line (for the cross

almost zero. However, for the validation point A which is one

of the cross class, its posterior probability in the dotted line (for

class) is almost one and its posterior probability in the solid line

zero.

e R function for LDA

R function for LDA is in the library MASS and is named as lda.

x is shown below, where x is a matrix (data frame) for a data set

formula “class ~.” defines the relationship (~) between a