1 Bayes' Decision Theory : Bayes' decision theory is the foundation for optimal pattern classifier design, and pro- vides the "fundamental equation" for modern speech recognition. The theory quantifies the concept of "accuracy" in pattern classification and recognition in statistical terms. That is, it defines the measure of accuracy in terms of the minimum expected risk, which can be achieved via the use of the Bayes decision rule.

doi:10.1201/9781482276237-35

Chapter

Chapter

ABSTRACT

For specific applications including speech processing, the risk function can be reasonably chosen to be zero or one: rti = 1 for i # j and r22 = 0. Now, Eq. 6.1 can be simplified to

Then, the generic decision function design given by Eq. 6.3 becomes

C(x) = CZ if and only if P(Ci Ix) = msx P(Ci Ix). (6.5)

This is often more concisely written as

C, = arg mcax P(C3 1x), (6.6)

where arg max is an operation that finds the argument maximizing the function that follows.