Abstract
In this chapter we continue the theory of classification developed in Chapter 5 on a somewhat more general level. We start out with some basic consideration of optimality. In the notation introduced in Section 5.4, Y will denote a p-variate random vector measured in k groups (or populations). Let X denote a discrete random variable that indicates group membership, i.e., takes values 1, … , k. The probabilities
will be referred to as prior probabilities, as usual. Suppose that the distribution of Y in the jth group is given by a pdf f j (y), which may be regarded as the conditional pdf of Y, given X = j. Assume for simplicity that Y is continuous with sample space ℝp in each group. Then the joint pdf of X and Y, as seen from Sec tion 2.8, is
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Flury, B. (1977). Discrimination and Classification, Round 2. In: A First Course in Multivariate Statistics. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2765-4_7
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DOI: https://doi.org/10.1007/978-1-4757-2765-4_7
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