Page 69 - Introduction to Statistical Pattern Recognition
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Chapter 3
HYPOTHESIS TESTING
The purpose of pattern recognition is to determine to which category or
class a given sample belongs. Through an observation or measurement pro-
cess, we obtain a set of numbers which make up the observation vector. The
observation vector serves as the input to a decision rule by which we assign the
sample to one of the given classes. Let us assume that the observation vector
is a random vector whose conditional density function depends on its class. If
the conditional density function for each class is known, then the pattern recog-
nition problem becomes a problem in statistical hypothesis testing.
3.1 Hypothesis Tests for Two Classes
In this section, we discuss two-class problems, which arise because each
sample belongs to one of two classes, o1 or 02. The conditional density func-
tions and the a priori probabilities are assumed to be known.
The Bayes Decision Rule for Minimum Error
Bayes test: Let X be an observation vector, and let it be our purpose to
determine whether X belongs to o1 or 02. A decision rule based simply on
probabilities may be written as follows:
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