What does Bayes Decision Rule have to do with Pattern Recognition?

Let’s consider a three dimensional binary feature vector *X*=(*x _{1}*,

and lets say that the prior probability for class 1 is *P*(*ω _{1}*)= 0.6 while for class 2 is

Additionally, we know that likelihoods of each independent feature is given by *p* and *q* where:

*p _{i} = P*(

meaning that we know the probability (or likelihood) of each independent feature given each class - these values are known and given:

*p* = {*0.8*,* 0.2*,* 0.5*} and *q *= {*0.2*, *0.5 *, *0.9*}

therefore, the discriminant function is *g*(x) =* g _{1}*(x) -

however, since the problem definition assumes that *X *is independent, the discriminant function can be calculated by:

After inputting the *x _{i}* values into the discriminant function, the answer

All points above the plane belong to class *ω _{2}* since if